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Impact on HDPE and PVC plates – Experimental tests and numerical simulations
Abstract
This paper presents first material tests on HDPE and PVC, and subsequently impact tests on plates made of the same materials. Finally, numerical simulations of the plate impact tests are compared with the experimental results. A rather comprehensive series of mechanical material tests were performed to disclose the behaviour of PVC and HDPE in tension and compression. Quasi-static tests were carried out at three rates in compression and two in tension. Digital image correlation, DIC, was used to measure the in-plane strains, revealing true stress–strain curves and allowing to analyze strain-rate sensitivity and isotropy of Poisson's ratio. In addition, dynamic compression tests were carried out in a split-Hopkinson pressure bar. Quasi-static and dynamic tests were also performed on clamped plates made of the same PVC and HDPE materials, using an optical technique to measure the full-field out-of-plane deformations. These tests, together with the material data, were used for comparative purposes of a finite element analysis. A reasonable agreement between experimental and numerical results was achieved.
... However, for polymeric materials measurements of the true tensile stress-strain are difficult, in particular, when neck propagation and volumetric plastic strains are present during the deformation process. It seems that only optical-based systems should be used for a reliable material characterization when dealing with polymeric materials, as one can confirm from the literature [4][5][6][7][8][9][10]. ...
... A more in-depth description of the test procedure can be seen in the work of Grytten et al. [24]. Other alternatives (e.g., introduction of a smooth notch [5,7] or a geometrical imperfection [4,6,8]) have been used to define the ''critical'' section. ...
... Indeed, the uniaxial tensile test loaded at a nominal strain rate of 2 3 10 À2 s À1 is considered in this work. A fullfield measurement of deformation is important because many polymers present volumetric plastic contribution during plastic flow [4,[6][7][8][9][24][25][26][27] requiring the monitoring of the actual cross section for true stress calculations purposes. ...
The methodology proposed in this work uses the local measured strain rate history as the applied “load” to the finite element (FE) “material point”. Next, with this strain rate history, two objective functions related to the true stress–strain and volumetric strain response could be minimized to identify some of the material parameters of the constitutive model. The whole identification process, of the nine material parameters required, is described in detail. In addition, a short description of the hyperelastic-viscoplastic constitutive model used is given with an experimental program including mainly uniaxial tensile tests at different strain rates. The thermoplastic material investigated here is a mineral and rubber modified polypropylene (PP) compound. The main experimental data uses 3D digital image correlation (DIC) to determine full-field displacements and deduce true stress–strain, volume dilatation, and local strain rates curves during deformation. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers
... The HDPE is a semicrystalline thermoplastic that contains considerably fewer particles. Results from uniaxial tension and compression tests have earlier suggested that the PVC is highly pressure sensitive both with respect to yield stress and plastic dilation (Moura et al., 2010). The macroscopic dilation in the PVC is a result of microscopic void growth (Ognedal et al., 2014). ...
... Both materials were acquired as 10 mm thick extruded sheets from the supplier SIMONA. Although Moura et al. (2010) found a slight direction dependency regarding the mechanical behavior, good results have been obtained when isotropy is assumed (Moura et al., 2010;Ognedal et al., 2012). Both materials will therefore be treated as isotropic in this study. ...
... Both materials were acquired as 10 mm thick extruded sheets from the supplier SIMONA. Although Moura et al. (2010) found a slight direction dependency regarding the mechanical behavior, good results have been obtained when isotropy is assumed (Moura et al., 2010;Ognedal et al., 2012). Both materials will therefore be treated as isotropic in this study. ...
This paper addresses the deformation of axisymmetric tensile bars, made of mineral-filled PVC and HDPE, with and without pre-machined notch. The purpose of the study is both to investigate the mechanical behaviour under various stress triaxialities, induced by different notch radii, and the capabilities of a phenomenological constitutive model. The yield stress and the plastic dilation have been chosen as the key response parameters from the tests in order to evaluate the yield function and the flow potential of the constitutive model. It is found that the yield stress and the plastic dilation of the mineral-filled PVC are highly sensitive to hydrostatic pressure. The yield stress of the HDPE hardly changes, while the plastic dilation increases with increasing stress triaxiality. The experimentally observed plastic dilation of both materials is related to void growth. The constitutive model reproduces force-displacement relationships for both materials with reasonable accuracy. However, the numerical simulations underestimate the plastic dilation for high stress triaxialities.
... The macroscopic behaviour of the mineral-filled PVC addressed in this paper has been reported earlier (Moura et al., 2010;Ognedal et al., 2012). The tensile stress-strain curve shows a behaviour that is initially linear elastic before reaching a peak stress, which may be interpreted as a macroscopic yield stress. ...
... The stress-strain curves for the eight successful tests are shown in Fig. 3. The results are in accordance with earlier observations (Moura et al., 2010;Ognedal, 2012). All stress-strain curves show a linear elastic response up to a local stress maximum. ...
... The volume strain is calculated as e v = e + 2e t , assuming that the transverse strains in the width and thickness directions are the same (Moura et al., 2010). Fig. 4(a) shows the volume strain plotted against longitudinal strain. ...
The nucleation and growth of voids in mineral-filled PVC have been investigated through experimental and numerical studies. Uniaxial tensile specimens were deformed in tension to different elongation levels and then unloaded. The macroscopic strain fields were recorded by use of digital image correlation. After the test, the microstructure of the deformed specimens was investigated in a scanning electron microscope. It was found that the observed volume strain on the macroscale is related to void growth on the microscale. In addition, finite element simulations were performed on unit cell models representing the microstructure of the material in a simplified manner. The numerical simulations demonstrate macroscopic dilation as a result of void growth. Moreover, the numerical simulations indicate that the experimentally observed stress-softening response of the PVC composite material may result from matrix-particle debonding.
... Polymers are often regarded as pressure sensitive materials; a higher yield strength in compression than in tension is commonly observed. Another feature is that the volume changes during plastic deformation (Delhaye et al., 2010;Delhaye et al., 2011;Grytten et al., 2009;Mohanraj et al., 2006;Moura et al., 2010). Moreover, some polymers have a stress softening behaviour after the yield limit, while others experience monotonic hardening (G'Sell et al., 1992;Moura et al., 2010). ...
... Another feature is that the volume changes during plastic deformation (Delhaye et al., 2010;Delhaye et al., 2011;Grytten et al., 2009;Mohanraj et al., 2006;Moura et al., 2010). Moreover, some polymers have a stress softening behaviour after the yield limit, while others experience monotonic hardening (G'Sell et al., 1992;Moura et al., 2010). These are some characteristics a material model for thermoplastics should allow for. ...
... Isotropic transverse deformation, i.e. equal strains in the width and thickness direction, was assumed when calculating the true stress both in tension and in compression. This has earlier been shown to be a good approximation for these materials (Moura et al., 2010). ...
... These tests serve as an independent check of the capabilities of the model. This paper gives a brief presentation of material tests on a high-density polyethylene (PEHD), see Moura et al. [1] for further details. The results are used to calibrate the constitutive model described in details by Polanco-Loria et al. [2] [3], the model is employed in numerical simulations of impact of plates made of the same PEHD material, and the predictions are compared with experimental results [1].Figure 1 summarises the recently developed model [2]. ...
... This paper gives a brief presentation of material tests on a high-density polyethylene (PEHD), see Moura et al. [1] for further details. The results are used to calibrate the constitutive model described in details by Polanco-Loria et al. [2] [3], the model is employed in numerical simulations of impact of plates made of the same PEHD material, and the predictions are compared with experimental results [1].Figure 1 summarises the recently developed model [2]. The material response is assumed to have two Parts A and B, which represent the intermolecular and intramolecular strength, respectively. ...
... Two replicate tests were carried out when determining the true stress-strain curve at strain rate 10 x3 s x1 , seeFigure 2a. Another set of samples was used in the strain-rate tests [1]. The test results were used to determine the parameters in the constitutive model, and their values are given inTable 1 [8]. ...
This paper presents quasi-static and dynamic tests on circular clamped plates made of a PEHD thermoplastic. A brief review of the main results from a material test programme, involving tension and compression tests at different rates, is also provided. The results from the material tests are used to identify the coefficients of a recently proposed hyperelastic-viscoplastic constitutive model for thermoplastics, also outlined here. Finally, the model is employed in numerical simulations of the impact tests. It is shown that the model represents the force-displacement response of the experimental tests fairly well. Also, considering the quasi-static tests, a localized failure mechanism around the impactor is captured.
... This FE model was tested for convergence of FE results. The rectangular containers were made of high–density polyethylene plastic (HDPE) which was modelled as linear-elastic isotropic material [23]. The material properties of FE models are shown in Table 1. ...
... Dimension of a spherical container was 1.24 m diameter and 5 mm thickness. All containers were made of HDPE plastic [23] which was modelled as elasto-plastic isotropic material as shown in Fig. 5. The material properties are shown in Table 1. ...
Water-filled containers have long known for its structural characteristic of impact load absorption. This paper presents design of structures resisting to impact load resulting from a high-velocity tennis ball. One cubic meter water containers consisting of rectangular, cylindrical, and spherical water containers and water levels were studied for their stress distribution and deformation during maximum deformation period using finite element analysis in the ANSYS 15.0 software. The containers were modeled by using shell elements and made of elasto-plastic material of HDPE plastic. The filled water was model by using fluid elements. We found that as ball velocity increased, maximum von Mises stress increased. However, for post-yielding behavior, maximum von Mises stress approached a constant near yield stress of HDPE material. As ball velocity increased, deformation increased. When water level increased, maximum deformation decreased. For the rectangular and cylindrical containers, when the water level increased, the maximum von Mises stress increased. However, in the spherical container, as water level increased, the maximum von Mises stress was not significant change. Among three water-filled containers, the rectangular container has the highest efficiency in impact absorption, followed by the cylindrical container and the spherical container respectively.
... These curves show similar characteristics of yielding and plastic flow. These features are similar to those reported previously for many polymers [9,23,24]. It is well known that strain hardening of polyethylene can be attributed to both the molecular structure and crystalline formation [9]. ...
... For simplicity and practicability in engineering applications, the true stress-strain curves obtained from experimental data can be imported into Abaqus directly [6]. In view that the yield stress and the logarithm of strain rate is showing a strong exponential relationship in Figure 12 the Cowper-Symonds (C-S) model was applied to incorporate the strain-rate effect [24,29]. The existing Cowper-Symonds model can be written as: ...
Properties of extruded polymers are strongly affected by molecular structure. For two different semi-crystalline polymers, low-density polyethylene (LDPE) and ultra-high molecular weight polyethylene (UHMWPE), this investigation measures the elastic modulus, plastic flow stress and strain-rate dependence of yield stress. Also, it examines the effect of molecular structure on post-necking tensile fracture. The static and dynamic material tests reveal that extruded UHMWPE has a somewhat larger yield stress and much larger strain to failure than LDPE. For both types of polyethylene, the strain at tensile failure decreases with increasing strain-rate. For strain-rates 0.001–3400 s⁻¹, the yield stress variation is accurately represented by the Cowper–Symonds equation. These results indicate that, at high strain rates, UHMWPE is more energy absorbent than LDPE as a result of its long chain molecular structure with few branches.
... The nominal stress was calculated from the Instron load cell measurements, and nominal strain was obtained using the cross head displacement. 1 The tensile responses of LDPE, HDPE and UHMWPE at two strain rates are plotted in Fig. 2. Consider first the results at a nominal strain rate of 10 À2 s À1 (Fig. 2a). The HDPE shows the highest yield strength, and LDPE the lowest. ...
... Furmanski et al. [21] argued that for UHMWPE, there is a deviation from isothermal conditions due to adiabatic heating after 15% of strain, leading to significant softening at larger strains. In the current tensile 1 The experimental method used in this investigation did not allow the local measurement of true stress, true strain and true strain rate after the onset of necking, at which point the deformation becomes highly non-uniform. Hence, nominal stress, nominal strain and nominal strain rate are used to characterise the overall response of these ductile polymers to large deformations. ...
Ductile thermoplastics, for example Ultra High Molecular Weight Polyethylene (UHMWPE), are of interest for their impact energy absorbing capabilities. While the impact perforation mechanisms of metallic targets have been investigated in some detail, far less progress has been made towards understanding the impact resistance of ductile polymers. The aim of this investigation is to identify the relationship between the projectile tip geometry and impact energy absorption of semi-crystalline thermoplastics. The focus of the study is light-weight monolithic plates of extruded polymer impacted normally by rigid projectiles at velocities up to 100 ms−1. Three polymers will be considered: Low Density Polyethylene (LDPE), High Density Polyethylene (HDPE) and Ultra High Molecular Weight Polyethylene (UHMWPE). Polyethylene provides a convenient test material, as variations in microstructure provide a contrast in mechanical properties, without significant variations in density. Three distinct projectile nose shapes are considered: blunt, hemi-spherical and conical. For a conical tip, perforation occurs by ductile hole expansion. For this nose shape the high yield strength and strain rate sensitivity of HDPE offers an advantage over the other two polyethylenes. Perforation by blunt and hemi-spherical projectiles is more sensitive to deformation localisation. The high strain hardening of UHMWPE, which increases with strain rate, results in a significantly greater impact resistance than either HDPE or LDPE. The perforation mechanisms and energy absorption of these PE plates are contrasted with those of thin aluminium alloy targets that have the same total mass. UHMWPE outperforms these metallic targets for all three projectile nose shapes. Finally, the influence of target thickness on the impact perforation of LDPE is considered. All three nose shapes show a linear increase in perforation energy with target thickness.
... Material t εɺ (s -1 ) E (GPa) ρ (kg. m -3 ) ν s r (mm) β (°) Ref. 316L stainles s steel 5600 200.0 a 7620 0.28 a 3.5 5 A [17] Met- als Iron 3162 100.0 b 7150 b 0.27 c 3.0 9 B [18] PMM A 100 3.2 1183 d 0.35 e 6.3 14 [19] PVDF 120 2.1 1780 0.35 1.9 15 C [20] RTM-6 resin 164 2.5 1140 0.38 4.5 25 [21] Nylon 6 100 2.3 f 1245 f 0.40 4.0 15 C [22] Nylon 66 100 2.4 g 1215 h 0.40 5.0 15 C [22] PVC 50 3.0 1430 0.42 i 6.5 15 C [23] Poly mers HDPE 87 0.8 950 0.47 i 6.5 17 [23] SiC 967 415.0 j 3160 j 0.16 j 3.1 30 D [24] Si 3 N 4 400 310.0 j 3290 j 0.27 j 3.1 30 D [24] AlN 1450 320.0 3250 0.24 2.3 30 D [25] SiC 1000 470.0 3200 0.20 3.6 30 D [26] Ce- ram- ics SiC 300 460.0 3200 0.16 4.0 30 D [27] Con- crete 63 37.9 2405 0.18 k 25.5 40 E [28] Con- crete 53 32.0 2323 k 0.20 20.0 40 E [29] Con- crete 126 23.0 2300 0.17 20.0 40 E [30] Mortar 100 20.0 2000 0.20 6.0 50 [9] Con- crete -like ma- teri- als Mortar 23 17.2 2179 0.19 37.0 40 [13] Barre granite 55 46.1 2619 0.30 l 3.2 69 [31] Coal 63 3.7 1469 0.40 5.8 50 F [32] Tuff 76 5.4 m 1700 0.19 m 6.2 50 F [33] Lime- stone 45 24.0 2300 0.30 l 6.3 50 F [34] ...
... Material t εɺ (s -1 ) E (GPa) ρ (kg. m -3 ) ν s r (mm) β (°) Ref. 316L stainles s steel 5600 200.0 a 7620 0.28 a 3.5 5 A [17] Met- als Iron 3162 100.0 b 7150 b 0.27 c 3.0 9 B [18] PMM A 100 3.2 1183 d 0.35 e 6.3 14 [19] PVDF 120 2.1 1780 0.35 1.9 15 C [20] RTM-6 resin 164 2.5 1140 0.38 4.5 25 [21] Nylon 6 100 2.3 f 1245 f 0.40 4.0 15 C [22] Nylon 66 100 2.4 g 1215 h 0.40 5.0 15 C [22] PVC 50 3.0 1430 0.42 i 6.5 15 C [23] Poly mers HDPE 87 0.8 950 0.47 i 6.5 17 [23] SiC 967 415.0 j 3160 j 0.16 j 3.1 30 D [24] Si 3 N 4 400 310.0 j 3290 j 0.27 j 3.1 30 D [24] AlN 1450 320.0 3250 0.24 2.3 30 D [25] SiC 1000 470.0 3200 0.20 3.6 30 D [26] Ce- ram- ics SiC 300 460.0 3200 0.16 4.0 30 D [27] Con- crete 63 37.9 2405 0.18 k 25.5 40 E [28] Con- crete 53 32.0 2323 k 0.20 20.0 40 E [29] Con- crete 126 23.0 2300 0.17 20.0 40 E [30] Mortar 100 20.0 2000 0.20 6.0 50 [9] Con- crete -like ma- teri- als Mortar 23 17.2 2179 0.19 37.0 40 [13] Barre granite 55 46.1 2619 0.30 l 3.2 69 [31] Coal 63 3.7 1469 0.40 5.8 50 F [32] Tuff 76 5.4 m 1700 0.19 m 6.2 50 F [33] Lime- stone 45 24.0 2300 0.30 l 6.3 50 F [34] ...
The transition strain-rate represents the start of significant contributions from radial inertia-induced lateral confinement to the axial compressive strength of the tested materials. However, it has been misinterpreted for decades by many studies as the start of significant strain-rate effect on the dynamic uniaxial compressive strength of the tested materials. Based on the dimensional analysis and numerical and experimental data, a semi-empirical formula to determine the transition strain-rates for various engineering materials is proposed. Errors in SHPB tests due to the contribution of the lateral confinement effect are estimated. It is found that, except for metals, transition strain-rates of concrete-like, rock-like and polymeric materials are unfortunately located in the valid range of SHPB tests that has been commonly accepted by research communities. Thus SHPB tests cannot be treated as valid measurements under uniaxial stress state when strain-rates are greater than the transition strain-rate.
... In addition to the possible change of volume, polymers are also known to exhibit other properties different from some other classes of materials. One example is a significant rate sensitivity [6][7][8][9][10][11]. Another is that the flow stress is dependent on hydrostatic pressure [5,8,9]. ...
... In addition to the possible change of volume, polymers are also known to exhibit other properties different from some other classes of materials. One example is a significant rate sensitivity [6][7][8][9][10][11]. Another is that the flow stress is dependent on hydrostatic pressure [5,8,9]. ...
The paper presents an experimental investigation of a semi-ductile rubber-modified polypropylene reinforced by mineral particles. The behaviour of the material is investigated by performing tension, shear and compression tests at quasi-static and dynamic strain rates, applying digital image correlation for full-field strain measurements. Subsequently, scanning electron microscopy is used to analyse the fracture surfaces of the tension and compression test samples, and to relate the observed mechanical response to the evolution of the microstructure. The experimental study shows that the material is highly pressure and strain rate sensitive, and that the rate sensitivity seems to be more pronounced with increasing pressure from tension via shear to compression. It also exhibits significant volume change, which is mainly ascribed to a cavitation process appearing during tensile deformation. Assuming matrix-mineral particle debonding immediately after yielding and self cavitation of rubber particles, both kinds of particles might be the source of initial cavities. From the study of the fracture surfaces in tension it appears that the fracture process is less ductile at high strain rates than under quasi-static conditions, while the micrographs taken of compression samples show that the size of the cavities is much smaller than in tension.
... It is taken into account that the compression springs can deform linear-elastically up to a deformation s_lim of 15 mm with the spring stiffness k_spring until the springs are fully compressed. The plastic window frames (PVC-U) and the protective films (BO-PET) are shown with corresponding elastic-plastic material formulations [3,4]. The brittle failure of the frame corners of the sash frame is described using element erosion. ...
In light of terrorist attacks and accidents, the need for structural protection against explosive events has increased significantly in recent decades. Conventional unprotected windows pose a particularly high risk for injury to building occupants due to glass fragments or even whole window frames being propelled into the interior and exterior of a building. A common approach of retrofitting is the application of anti-shatter films in combination with a catcher-cable system. The protection effect and efficiency of these measures was investigated with a series of shock tube tests by the authors and published. The present paper focusses on the cable catcher system that retain fragments of the window on the inside of the room. The impact and the forces as well as the deformations occurring in the steel cables are investigated using analytical and numerical methods. The findings are compared with the shock tube tests and it appears that there is a good agreement. As a result, the finite element simulations enable a detailed representation of the impact process and are suitable for the design of such structural protection measures. Furthermore, practical considerations using catcher-cable systems and application limits of the combined use with anti-shatter films for blast protection are discussed.
... Furthermore, the model can simulate the exact brittle response of the polymer at high strain. The stress-strain curve used in this study is obtained by [19]. The equation can be expressed as: ...
An experimental protocol was developed to predict the service period of polyethylene pipes under high loads. This paper presents the results of field test of chimney demolition loading to polyethylene pipeline, and compared with the numerical simulation. Combined with the practical engineering situation, the ground impact load first propagates to the explosion-facing side of the pipeline, and the effect was found to decrease as the applied stress decreased, however, under high impact load, ring strain tends to be greater than axial strain. The test data such as vibration velocity and frequency are processed to determine the damage characteristics needed to protect the pipeline from damage. Finally, the safety assessment of pipeline under impact load was determined by yield criterion.
... These features are similar to those reported previously for many polymers. 11,12 It is well known that strain hardening of polyethylene can be attributed to both the molecular structure and crystalline formation. 13 Furthermore, we see that coal ash/recycled HDPE specimens are sensitive to strain rate. ...
In this study, coal ash/recycled plastic composite material was fabricated with post-consumer
high-density polyethylene (HDPE) and coal ash particles. The main idea of using coal ash, since it
is also a waste product, as reinforcing ¯ller in recycled HDPE is to reduce the cost, develop
lightweight and produce environmental-friendly materials. Coal ash/recycled plastic composite
have been used in signi¯cant applications as construction materials including °ooring, landscaping, fencing, railing window framing and roof tiles. E®ect of coal ash loading on the mechanical properties and thermal conductivity of coal ash/recycled HDPE composite were
determined. It is expected to use waste materials in new ¯eld by getting novel composite materials
with developed mechanical properties. It was found that coal ash ¯ller indicated signi¯cant
improvement on the mechanical properties of composites. The results show that the impact
decreased tremendously from 57.32 to 15.8 kJ/m2 with only 30 wt.% loading of coal ash. The ¯ller
increases the elasticity of the material and reduces its ability to absorb deformation energy.
... Furthermore, the model can simulate the exact brittle response of the polymer at high strain. The stress-strain curve used in this study is obtained by Ref. [36]. The equation can be expressed as: ...
The blasting vibration load can pose great threats to the safety of urban buried pipelines. Winkler model is commonly used to simulate the soil-pipe interaction and calculate the response of the stiff pipe, but the effectiveness of the resulting for the flexible pipe is doubtable. In this study, a theoretical method based on the Winkler model and the Timoshenko beam theory is presented to calculate the effect of blasting load induced by rock blasting on the overlying flexible buried pipe, and the modified soil spring stiffness is provided for accurately calculating the vibration response of flexible high-density polyethylene (HDPE) pipe buried in the silty clay. The proposed theoretical method and modified spring stiffness are tested and calibrated against full-scale experiments and its detailed numerical modeling with ANSYS/LS-DYNA. It is indicated that the analytical method with empirical spring stiffness (from American Lifeline Alliance 2001) overestimates the vibration velocity magnitude of the HDPE pipe subjected to blasting vibration. Reducing the spring stiffness to one-tenth of the original value can provide improved calculation results for flexible HDPE pipe subjected to blasting vibration.
... Nevertheless, as a matter of fact that the onset of crazing which is the actual reason for damage in rubber toughened amorphous thermoplastics like ABS causes voids near rubber particles which may result in a volume change during deformation [75]. Consequently, the volume change needs to be taken into consideration in the determination of tensile true stress-true strain behavior of amorphous thermoplastics [76][77][78][79][80][81]. ...
... After the limit point of elasticity, the stress goes through a maximum corresponding to ultimate stress "s u " followed by a plastic deformation until rupture. 53,54 The aging temperature has an impact on mechanical properties. The slope of the elastic part of the curve increases remarkably from 25 C to 90 C, showing a stiffening arise of the material. ...
In this paper, an experimental study was conducted to characterize industrial PVC pipes and to investigate the effect of hydrothermal aging on their physico-chemical, thermal, and mechanical behavior. Three temperature (25°C, 60°C and 90°C) and full immersion in distilled water were retained as accelerated hydrothermal conditions. Kinetic of water absorption was examined and Fickian behavior was observed. The aging temperature was found to influence the water uptake behavior of PVC samples. Thermogravimetric analysis (TGA) has proved that the pipe material is not pure, while it consists of PVC reinforced with calcium carbonate (CaCO 3). After exposure to accelerated aging, TGA and FTIR analysis exhibit preliminary signs of degradation of PVC samples under the retained conditions. Changes affecting the shape and the color of aged samples were examined. Mechanical properties have been characterized, after immersion of 30 days, with an improvement of strength and stiffness of the aged samples, in particular at elevated aging temperature. However, the aging response is accompanied by a loss of ductility for the aged material. These results, even for brief exposure, could help to understand the behavior of PVC composite pipes under hydrothermal conditions.
... The legend icons under the figure 2 show different matter state of the projectile and target fragments. Under the picture there are a brief transcriptions of these conditions: SHEAR -the material is destroyed as shear; the SPALL -a material is failed as a separation; MELTING -the internal energy of the medium is above the melting energy; P GAS -internal energy of a material is above the sublimation energy; GAS -the substance is in a steamed condition [15][16][17][18][19][20][21][22][23][24]. Further, elimination of the evaporated fragments allows to simplify the calculation and analysis of the problem [25][26][27][28]. ...
The paper discusses the results of the numerical simulation of high-speed impact effect of compact projectiles made of steel and tungsten alloy with steel obstacles of equal mass. The obstacles have different initial porosity of the material. Conducted the final evaluation of the penetration speed of the projectile depending on the porosity of the obstacle and the initial speed of the shock interaction. The initial impact velocity range from 1 to 16 [km/s]. The destruction, melting and evaporation of the interacting bodies are taken into account. The analysis of porosity influence evaluation of obstacles material revealed that the protective advantage of porous obstacles disclose at the higher impact velocities, greater than 1.5 [km/s] for steel strikers and 2 [km/s] for projectiles of tungsten alloy. The more impact velocity the more protective effect of porous obstacles.
... In last years, the use of polymer increased in automotive and medicine industry since it is light, formable, cheap, good resistant to corrosion, nontoxic, and flexible for all these characteristics in many applications replacing metal by polymer. Polymers are experiencing an increased use in load carrying components, and this is due to the low density and high-energy absorption skills of the polymer [1]. In this research we employed linear low-density polyethylene (LLDPE), density amount is 0.930 gm/cm^3 and melting temperature Tm (110-137) Celsius degree [2]. ...
In general, the manufacture of plastic materials is commonly in the world due to their applications. Plastic is light weight, cheap, and able to be used in different industries, for example parts of automotive and home tools. This research represents a challenge on how to design and manufacture a changeable mold. First, a mold was designed by the Auto CAD program and then manufactured in the workshop. The mold consists of three parts, the middle part has changeable cavity. The mold was cooled by worm net pipes embedded into the third part. All specimens were manufacture in this mold. The injection plastic flow is perpendicular on mold. The goals of this research are to design and manufacture a mold and to determine the mechanical properties of linear low density polyethylene. Three types of test were executed, tensile, impact and bending. The results of tensile test showed that the tensile strength value is 15 MPa, Young’s modulus is 0.18 GPa, yield stress is 12 MPa, and Elongation to break is 70.88 mm. From impact test, the impact strength is about 193.75 KJ/m2, while in bending test, the flexural strength is about 18 N/mm2 and the shear stress is 1.5 N /mm2.
... For what concerns the strain-rate effect, the Cowper-Symonds model (the term within square brackets in eq. (4)) was found acceptable for many semi-crystalline and amorphous polymers [26][27]. ...
Modelling the mechanical behaviour of plastics in the simulation of phenomena involving large strains and large displacements, as in crash simulations, is a complex task due to the highly non-linear characteristics of these materials. Moreover, non negligible influences of strain-rate, multiaxial loading, and temperature are present and must be taken into account accordingly. This work presents some results about the modelling of these effects for a thermoplastic used in automotive components. The model was developed based on experimental results obtained in different loading conditions, with different temperature and strain-rate. The time factor was investigated both in short term loading (dynamic loading) and long term tests (creep loading). Both these loading cases are very important in plastic parts design.
... Using LS-DYNA software [26], an explicit nonlinear structural integration scheme was applied to analyze the dynamic response of the incident bar. The code has been validated to analyze the dynamic response such as in SHPB experiments [27,28]. The striker was meshed with 9216 eight-node brick elements, and the incident bar was meshed with 384000 eight-node brick elements. ...
Experimental and numerical simulations were undertaken to estimate the effects of imperfect conditions on stress waves in split Hopkinson pressure bar (SHPB) experiments. The photonic Doppler velocimetry (PDV) measurement results show that the rise and fall times of an incident wave increases with an increasing inclination angle; also, the fluctuations of the incident wave disappear gradually with the increase of inclination angle. The following characteristics for various defects in the SHPB were obtained by numerical simulation: (1) the influence of a curved bar was negligible; (2) misalignment modestly affects the fluctuation characteristics, and bending waves were generated at this condition; (3) inclination and indentation of the impact end-surface had a great impact on the incident waves, and both of them increase the rise time of the incident wave by increasing the degree of defects. In view of the results, misalignment, inclination, and indentation in SHPB experiments should be minimized. © 2015 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
... Lademo et al. [28] studied a bumper system and proposed a new material model considering the influence of forming operations that often involve aluminium extrusions. Polanco-Loria [38] proposed a constitutive model for thermoplastics and Moura et al. [33] studied the behaviour of a rubber-particle-reinforced polypropylene. Du Bois et al. [13] made a comparative review of material models for polymers with a special focus on crashworthiness analysis. ...
Preformed structural reinforcements have shown good performance in crash tests, where the great advantage is their weight. These reinforcements are designed with the aim of increasing the rigidity of regions with large deformations, thus stabilising sections of the vehicle that work as load path during impact. The objective of this work is to show the application of structural reinforcements made of polymeric material PA66 in the field of vehicle safety, through finite element simulations. Simulations of frontal impact at 50 km/h and in ODB (offset deformable barrier) at 57 km/h configurations (standards such as ECE R-94 and ECE R-12) were performed in the software LS-DYNA® and MADYMO®. The simulations showed that the use of polymeric reinforcements leads to a 70% reduction in A-pillar intrusion, a 65% reduction in the displacement of the steering column and a 59% reduction in the deformation in the region of the occupant legs and feet. The level of occupant injuries was analysed by MADYMO® software, and a reduction of 23.5% in the chest compression and 80% in the tibia compression were verified. According to the standard, such conditions lead to an improvement in the occupant safety in a vehicle collision event.
... This causes different pulse shapes and hence different strain rates. For each fixed pressure, 1 to 4 tests were performed, DYMAT 2009 and the results are depicted in Figure 3 together with the quasi-static stress-strain curves for this material [10]. Note that the curves represent true stress-log strain values, obtained after standard correction from the engineering values. ...
Dynamic compressive curves of high density semi-crystalline polyethylene, PEHD, were obtained via the Split Hopkinson Pressure Bar, SHPB, technique. The SHPB was fitted with polymeric bars, PMMA, to avoid a large impedance mismatch between the specimens and the bars. As a consequence, attenuation and dispersion had to be taken into account. Care was also exercised with frictional effects by using ring specimens instead of flat disks. Ring specimens have the additional advantage of yielding a more constant strain rate in the tests. The results clearly show a very strain rate sensitive material, a feature which should be taken into consideration when analysing PEHD components.
In this research, a directional reduction charging structure was proposed to solve the problems caused by drilling and blasting method such as serious damage to surrounding rocks, working face low contour flatness and serious over-under break of root base c. Drilling and blasting tests, numerical calculations and field applications were designed and performed for the verification of the blasting advantages of charge structure. Test results showed that the peak positive strain along the protection direction of directional protection shaped charge was significantly smaller than that of ordinary charge, where PVC material presented the strongest effect such that the peak positive strain of specimen 1 at measuring point 4 (protection direction) was only 0.27 times that at measuring point 9 (non-protected direction). Numerical simulations indicated shaped jet formation, damage-reduction and charge penetration process and obtained the force law of cement target plate. Experimental results revealed that application of charge in tunnel controlled blasting achieved a clear controlling effect on contour line excavation. Compared with ordinary smooth blasting method, all technical indicators of the developed method were improved such that half hole mark rate was increased by about 33% and the amount of over-under break was decreased by about two times. Research results are of certain significance for the stability of surrounding reserved rocks and formation of roadway in blasting engineering and the developed method was found to be applicable to mining, shaft excavation and other projects.
Explosionen stellen eine erhebliche Bedrohung für Gebäude dar, insbesondere für herkömmliche, ungeschützte Fenster. Dieser Beitrag befasst sich mit Seilauffangsystemen, die Bruchstücke des Fensters rauminnenseitig auffangen. Der Aufprall sowie die auftretenden Kräfte und Verformungen in den Stahlseilen werden mit numerischen und analytischen Methoden untersucht und mit Versuchsergebnissen aus Stoßrohrversuchen verglichen. Numerische Simulationen ermöglichen eine detaillierte Abbildung des Aufprallvorganges und eignen sich zur Bemessung von derartigen baulichen Schutzmaßnahmen.
The shape of a charge liner used in shaped charges with a combined liner will greatly influence the blasting effect. In this study, we examined how combined charge liners with different shapes affected directional rock blasting, and we assessed the influence mechanism. The numerical simulation results showed that among the three shaped charge liners, liners with arc and triangular shapes performed significantly better than the flat‐top liner, and the triangular liner was slightly superior to the arc‐shaped liner. Model testing indicated that principal cracks in the arc‐shaped and triangular liners developed along the combined energy‐gathering direction, while the principal cracks of the flat‐top liner deviated 32° from the axis. Therefore, the directional cracking effect of arc‐shaped and triangular liners was superior to the flat‐top liner. According to the peak strain values on the liners, the peak strain in the combined energy‐gathering direction was greater than that in the slot and nonenergy‐gathering directions, and the order of the peak strain of the three liners followed arc‐shaped liner > triangular liner > flat‐top liner. The directional blasting effect of the triangular liner was slightly better than the arc‐shaped liner. In conclusion, the findings of this study suggested that the best directional rock‐blasting effect was achieved when the shape of the combined charge liner was triangular.
This paper presents experimental and numerical studies on the damage mode of the strand cables under explosions, followed by an assessment of the residual capacity of the blast-damaged cables. Field blast tests were carried out to obtain the damage profile and dynamic response of four strand cables considering different charge weights and standoff distances. The numerical model was established in LS-DYNA, in which the strands were innovatively simulated by the equivalent beam-shell model. The finite element model was then validated by the test results. The experiments revealed that the strand cable presented a whiplash motion under blast loading and the remaining force in the cable was proportional to the number of remaining strands. The damage of the strands can be classified into three levels according to the experimental observations, providing the basis for the prediction of its residual capacity. Based on the validated model, parametric studies were conducted to investigate the influence of prestressing force, cable dimension, charge weight, and standoff distance on the damage degree of strand cables. An empirical formula was then derived through multi-variable regression analysis, which could accurately predict the residual capacity of strand cables after explosions. The empirical formula can be used for the preliminary blast-resistant design of strand cables, emergency disposal of blast-damaged cables, and also provides a reference for the risk assessment of cable-stayed structures.
Hybrid composite materials combine different fibers in preform and take advantages of different mechanical behaviors for improving ballistic impact damage tolerances. Here we report ballistic impact damages of plain-woven laminates with different hybrids and stacking sequences. Three kinds of hybrid laminates, i.e., carbon/Kevlar, carbon/ultra-high molecular weight polyethylene (UHMWPE), and UHMWPE/Kevlar, had been prepared and tested in ballistic penetration with fragment simulating projectiles (FSP). The residual velocities of the projectiles and impact damage morphologies of the laminates have been obtained to show impact energy absorptions for the different hybrid schemes. A microstructural model of the hybrid laminates had also been established to show impact damage mechanisms with finite element analysis (FEA). We found that the UHMWPE/Kevlar hybrid laminates with Kevlar layers as the front face have the highest energy absorption capacity, followed by the carbon/Kevlar hybrid laminates with carbon layers as the front face. The main damage modes are fiber breakages, matrix crack and interlayer delamination. The ballistic damage evolutions from the FEA results show that the major damage is shear failure for front layers, while tension failure for the back layers. We expect that the ballistic impact performance could be improved from the different hybrid schemes.
With the global threat of terrorism on the rise, the protection of important infrastructure such as cable-stayed bridges from terrorist assaults has become a major concern. In cable-stayed bridge designs, the cables are crucial load-carrying components, and their failure could result in the progressive collapse of the bridge with catastrophic results. However, there is very limited understanding of the blast effects on cables. This paper presents a study on the blast performance of parallel wire cables under contact explosions. Field blast tests were conducted on four identical parallel wire cable specimens with varying charge weights and prestress levels. Arbitrary-Lagrangian-Eulerian (ALE) algorithm is utilized to develop the numerical model in LS-DYNA. The numerical model is then validated and further used to investigate the damage mechanism of the cable under contact explosions. The results indicate that the damage process of cables under contact blasts can be divided into three stages: Compression, divergence, and stretching. The wires arranged in angular points facing the detonation are particularly vulnerable, and high-density polyethylene (HDPE) is prone to be pelted off by explosive pressure. Parametric analyses were carried out to investigate the influences of charge weight and prestressing force on the damage degree of cables. The relationship between the TNT equivalent and the number of fracture wires is derived from the parametric analysis results. Furthermore, the prestress is found to have a considerable impact on the degree of cable damage induced by contact explosions. Taking prestress into account, a damage evaluation method for blast-damaged cables is proposed.
Two dynamic Brazilian tests are analyzed via digital image correlation for acquisition rates equal to 5 and 10 million frames per second. Displacements of the order of 1 mm, velocities of the order of ± 250 m/s, and accelerations as high as ± 4 × 10 ⁷ m/s ² are measured with spacetime DIC. Uncertainty quantifications enable spacetime DIC to be compared with instantaneous analyses. The gains provided by the temporal regularization are very significant for the acceleration fields. The observed levels are consistent with a priori estimates.
The impact behaviour of polyethylene plate has been experimentally and numerically investigated. The analysis involves determination of the ballistic impact behaviour of polyethylene plates under dynamic impact of rigid conical nose shape projectile. The experimental investigation has been carried out using pneumatic gun set-up with arrangements for recording the impact velocity and residual velocity after perforation. The experimental investigations, are supplemented with the numerical analysis based on FE code using ABAQUS/EXPLICIT. Mie-Gruneisen equation of state is employed for modelling of the problem. A detailed analysis has been presented to explore the mode of deformation, ballistic limit and the failure characteristics of the polyethylene plate under normal impact of conical projectiles.
The paper discusses the results of the numerical simulation of high-speed impact effect of compact projectiles made of steel and tungsten alloy with steel obstacles of equal mass. The obstacles have different initial porosity of the material. Conducted the final evaluation of the penetration speed of the projectile depending on the porosity of the obstacle and the initial speed of the shock interaction. The initial impact velocity range from 1 to 16 [km/s]. The destruction, melting and evaporation of the interacting bodies are taken into account. The analysis of porosity influence evaluation of obstacles material revealed that the protective advantage of porous obstacles disclose at the higher impact velocities, greater than 1.5 [km/s] for steel strikers and 2 [km/s] for projectiles of tungsten alloy. The more impact velocity the more protective effect of porous obstacles.
In this paper we consider issues related to numerical modelling of processes of high-speed impact effect of a consistent series of damaging elements on the massive barrier. Research is carried out by comparing the finite speed of penetration of this series at a speed of penetration of the elongated one-piece (rod) of the missile of the same mass and diameter. Examines the range of initial impact speeds from 1 to 12 km/s taking into account such physical phenomena as fracture, melting and evaporation of the interacting bodies. The analysis showed that almost in all range of impact speeds segmented drummer is better solid elongated.
This article presents the most common tests used to infer the mechanical response of materials (i.e., the material stress-strain curve). Different techniques are discussed, leading to measurement of the materials response in a wide range of strain rates, from quasistatic to very fast loading. The article begins with an appraisal of the importance of knowing the material strength. Basic concepts of strain and stress measures are introduced. Next, follows a detailed description of the tensile and compressive tests, side by side with the techniques used to measure the strains. Midrange-strain-rate devices are presented next, allowing one to obtain the material response necessary in various daily applications. High-strain-rate tests are then discussed next, with the detailed presentation of the main mechanical device used in these tests: the split Hopkinson pressure bar. Both compressive and tensile test devices are presented, as well as the basic equations used for data interpretation. Next follows a short section on constitutive laws, with the article finishing with a discussion on the various methods used, including indentation tests. The mechanical behavior of various materials is presented within the sections.
In quasi-static tension and compression tests of thermoplastics, full-field strain distribution on the gage section of the specimen can be captured using the two-dimensional digital image correlation method. By loading the test specimens made of a talc-filled and impact-modified polypropylene up to tensile failure and large compressive strains, this study has revealed that inhomogeneous deformation within the gage section occurs quite early for both test types. This leads to the challenge of characterizing the mechanical properties-some mechanical properties such as stress-strain relationship and fracture strain could depend on the measured section length and location. To study this problem, the true stress versus true strain curves determined locally in different regions within the gage length are compared. The results show that, for the tension test, the stress-strain curve seems independent of regions within the gage section, but the local fracture strain increases as the length of the measurement region is reduced. For the compression test, the large transverse expansion of the material in the middle of the gage section causes the specimen surface to become shorter and bulged out in the late stage of the tests, which makes the test result only reliable when the longitudinal strain is smaller than 0.2. A possible inverse-engineering method is proposed for identifying the true material response at a large compressive deformation. It is also shown that the ratio of longitudinal strain to transverse strain is different between tension and compression tests. This difference is not addressed in any existing material models in the finite element software LS-DYNA.
When a scaled structure (model or replica) is used to predict the response of a full-size compound (prototype), the model geometric dimensions should relate to the corresponding prototype dimensions by a single scaling factor. However, owing to manufacturing technical restrictions, this condition cannot be accomplished for some of the dimensions in real structures. Accordingly, the distorted geometry will not comply with the overall geometric scaling factor, infringing the Π theorem requirements for complete dynamic similarity. In the present study, a method which takes geometrical distortions into account is introduced, leading to a model similar to the prototype. As a means to infer the performance of this method, three analytical problems of structures subjected to dynamic loads are analysed. It is shown that the replica developed applying this technique is able to accurately predict the full-size structure behaviour even when the studied models have some of their dimensions severely distorted.
This paper proposes a method that allows a strain field on plane samples to be determined using the digital image correlation method. The displacement field is approximated by an iterative process attempting to optimize the correlation between two pictures, the first one before strain and the second one after strain. The precision obtained on the displacement field can be better than 0.01 pixel. This precision makes it possible to calculate the strains in a large range, from elastic strains (>0.01 per cent) to large strains (>200 per cent), with or without a strain gradient.
The dynamic response of elastic-plastic beams is studied numerically using several ma-terial constitutive models which take into account material strain hardening and strain-rate hardening. A comparison is drawn between the beam responses of these more sophisticated models and the ones predicted by a rigid, perfectly plastic material law. A method for choosing the material parameters in the bilinear model is proposed. The numerical simula-tion shows the importance of the elastic effect which reduces the plastic work absorption as well as causes part of the plastic work to be dissipated during vibration. The study reported here allows a better understanding of the influence of various material parameters on the dynamic response of structures and helps to establish some limits of validity for the rigid, perfectly plastic analysis.
In many polymers, including glassy thermoplastics and reinforced blends, it has been shown qualitatively that damage processes (crazing and cavitation) contribute to the apparent plastic deformation in addition to shear yielding. The aim of this paper is to determine more quantitatively their influence on the constitutive equation and/or on the kinetics of plastic instability. By using a novel video-controlled testing system, the evolution of volume strain is determined in polyethylene terephtalate (PET) and high-impact polystyrene (HIPS) by measuring in real time the three principal strain components in a small volume element, while the specimens are deformed under uniaxial tension at constant true strain rate. The contribution of volume strain to the overall true strain is 50% in the case of PET and nearly 100% for HIPS. Observation of sample geometry during complementary stretching tests at constant elongation rate show that necking is moderate in PET and completely absent in HIPS, although both polymers undergo stress drop at yield and nearly no strain hardening. This unexpected plastic stability is shown to be due to damage. In this scope, the classical theory of diffuse necking in polymers is revisited in order to take explicitly into account the damage rate, D, which expresses the slope of the volume strain vs. true strain curve.
Dynamic compressive curves of high density semi-crystalline polyethylene, PEHD, were obtained via the Split Hopkinson Pressure Bar, SHPB, technique. The SHPB was fitted with polymeric bars, PMMA, to avoid a large impedance mismatch between the specimens and the bars. As a consequence, attenuation and dispersion had to be taken into account. Care was also exercised with frictional effects by using ring specimens instead of flat disks. Ring specimens have the additional advantage of yielding a more constant strain rate in the tests. The results clearly show a very strain rate sensitive material, a feature which should be taken into consideration when analysing PEHD components.
The features profile of styrene-butadiene block copolymers (SBS) is strongly determined by their chemical structures. Three structural types have been commercially successful.
Materials are evolving faster today than at any time in history. As a consequence the engineer must be more aware of materials and their potential than ever before. In comparing the properties of competing materials with precision involves an understanding of the basic properties of materials, how they are controlled by processing, formed, joined and finished and of the chain of reasoning that leads to a successful choice. This book will provide the reader with this understanding. Materials are grouped into four classes: Metals, Ceramics, Polymers and Composites, and each are examined in turn. The chapters are arranged in groups, with a group of chapters to describe each of the four classes of materials. Each group first of all introduces the major families of materials that go to make up each materials class. The main microstructural features of the class are then outlined and the reader is shown how to process or treat them to get the structures (properties) that are wanted. Each group of chapters is illustrated by Case Studies designed to help the reader understand the basic material. This book has been written as a second level course for engineering students. It provides a concise introduction to the microstructures and processing of materials and shows how these are related to the properties required in engineering design. © Michael F. Ashby and David R. H. Jones 1998. All rights reserved.
In this chapter we present an overview of the high-temperature properties and applications of polymers and polymer composites. Included are discussions of heat transfer in polymer-based materials, their physical and mechanical properties at elevated temperatures, chemical and physical aging of polymers and effects of aging on properties, and the thermal and mechanical response in high-temperature, high-heat-flux environments. Finally, we present a brief discussion of modern high-temperature polymers and the effect of molecular structure on their properties.
The aim of the present work is the evaluation of mechanical properties of polymer and polymer matrix composites by using a low energy impact technique on a flexure plate configuration, which consists of a plate that is hit by a semi-spherical indenter. For the analysis of the force-time histories acquired experimentally a non elastic and non conserva-tive model that includes the permanent deformations due the flexion and indentation produced by the impact is proposed. The model proposed has two systems set up in a serial arrangement. The first one is a spring-dashpot and the second is a hertzian spring-dashpot that simulates the indentation. Since the differential equation that describes this system does not have an analytical solution a 4th order Runge–Kutta algorithm was used. The overall energy loss was calculated by means of the restitution coefficient that was measured experimentally; these results were compared with those obtained solving the differential equation. Eight sets of samples of polystyrene (PS) matrix composite with elastomeric and rigid dispersed phases were tested. A good correlation between the analytical and experimental results was observed, which allowed the calculation of the elastic modulus at high loading rates and the determination of the energy necessary to initiate damage of the specimen.
Polymer Engineering Science and Viscoelasticity: An Introduction provides a unified mechanics and materials perspective on polymers: both the mathematics of viscoelasticity theory, as well as the physical mechanisms behind polymer deformation processes. Written for advanced seniors seeking graduate level courses, first and second year graduate students and practicing engineers, this volume describes the relationship between mechanical properties and the basic molecular structure and mechanisms associated with the performance of structures made from polymer based materials. Clearly written in an organized manner, readers need only basic knowledge of solid mechanics and materials science in order to use this reference successfully. Introductory material on fundamental mechanics is included to provide a continuous baseline for readers from all disciplines. Introductory material on the chemical and molecular basis of polymers is also included, which is essential to the understanding of the thermomechanical response. This self-contained text covers the viscoelastic characterization of polymers including constitutive modeling, experimental methods, thermal response and stress and failure analysis. Example problems are provided within the text as well as at the close of each chapter.Polymer Engineering Science and Viscoelasticity: An Introduction provides an excellent overview suited to cross-disciplinary engineers and scientists who need to understand the basic background of polymeric behavior to rigorous mechanics approaches to the design of structures made with polymer based materials. © 2008 Springer Science+Business Media, LLC. All rights reserved.
Rate-dependent large deformation behavior of the alloy of polycarbonate and acrylonitrile–butadiene–styrene (PC/ABS) is experimentally investigated over a crosshead speed range of 1–3000mm/min. Three-dimensional non-contact digital image correlation (DIC) method is used to measure the large deformation of polymer specimens. Numerical simulation of geometry effect on the necking process of specimens is done for the specimen with two section sizes. It is found that the width contracts less than the thickness due to its larger size than the thickness for specimens with rectangular sections, and the relations between two lateral contraction ratios and engineering strains are geometry dependent, but independent of loading speeds. The influence of strain rates on local volume ratios of PC/ABS is also discussed. Based on the experimental results, a simple phenomenological constitutive model with six parameters is proposed for the glassy polymer, in which the effect of strain rate and its variation during constant crosshead speed loading tests is considered, and can be used in constant true strain rate or constant principal stretch rate loading condition.
The large-strain tensile behavior of polycarbonate and polycarbonate filled with several volume fractions (f) of rubber particles is studied via an optical technique. Digital image correlation is used to determine, in two dimensions, the local displacement gradients and full-field displacements during a uniaxial tension test. Full-field strain contours, macroscopic true stress–strain behavior, and local volumetric strain are reduced from the raw test data. Full-field strain contours exhibit a decreasing degree of localization with increasing f. The true stress–strain results show a decrease in modulus, yield stress, post-yield strain softening, and subsequent strain hardening with increasing f. The volumetric strain decreases with increasing f as well. In the case of the neat polymer, comparisons are made to a three-dimensional finite element simulation.
This note comments on a strain rate pattern found in tensile tests. This strain rate pattern readily suggests that the Cowper-Symonds equation relating the static and dynamic flow stresses with the strain rate is not valid for a broad range of strains unless its coefficients change. A modification of the Cowper-Symonds equation is proposed, and good prediction of the dynamic flow stress at any strain and strain rate level was obtained.
When a rigid armor piercing (AP) projectile impacts an inclined plate it can be deflected by the asymmetric forces, which the target exerts on the projectile. This is a well-known phenomenon which has been investigated by several workers impacting various metallic targets with AP projectiles. These works have shown that if the incidence angle is small enough the projectile can ricochet from any metallic target, provided the target is thick enough. In the present study we investigated the deflection, and ricochet, of 0.3″ AP projectiles impacting inclined polymeric targets, which, to our best knowledge, were not investigated before. We concentrate our attention on Plexiglas targets, which turned out to exert the strongest asymmetric forces on the AP projectile. We present a thorough 3D numerical study following the important properties of the target, which control the ricochet and deflection processes. It turns out that these properties are the high compressive strength and the low tensile strength of the target. In other words, the high brittleness of Plexiglas is responsible for the large deflection which was observed in our experiments. Other polymers, less brittle, resulted in a much lower effect or no effect at all.
An optical system using structured light and close-range photogrammetry for full-field continuous measurements of the out-of-plane deformation of a metal plate loaded at its centre by a moving punch is presented. The system is applicable both for quasi-static and dynamic loading conditions, but in this paper focus will be on the former. In the tests, a square AA5083-H116 aluminium plate is mounted in a circular frame and penetrated from above by a cylindrical punch, while the out-of-plane deformation is observed from below. A fringe pattern is projected on the target plate surface and recorded by a camera (or more than one if required). The changing fringe positions on the plate surface during perforation are then computer processed to give topography information of the out-of-plane deformation. This paper is divided into three major parts. First, the optical technique is presented with a description of the applied method, image analysis procedures, calibration of the system and estimation of accuracy of the acquired data points. The experimental set-up is then presented, and some results from a typical test where a 5mm thick plate with free-span diameter of 500mm is perforated by a 20mm diameter blunt-nose punch are given. Finally, numerical simulations of the perforation process are carried out using the non-linear finite element code LS-DYNA. The numerical predictions are compared with the experimental observations and the applicability of the experimental method is discussed based on the obtained results.
An optical system based on structured light and close-range photogrammetry has been developed and is in this study used to continuously measure the full-field out-of-plane deformation of aluminium plates subjected to low-velocity impact loading. During testing, square AA5083-H116 aluminium plates with thickness 5 mm were mounted in a circular frame and impacted by a 30 mm diameter blunt-nose projectile with velocities ranging from 7 to 11 m/s, while the out-of-plane deformations were measured at the opposite side. A fringe pattern was projected onto the rear target surface by a slide projector and the variation in the pattern during penetration was observed by a high-speed camera recording 10,000 images per second. The recorded images were subsequently computer processed to provide full-field topography information of the target surface during deformation. Degradation of measurement data due to impact induced vibration has been evaluated and reduced to a minimum by isolating the optical system from the mechanical experiment. The out-of-plane deformation measurements were compared to non-linear finite element simulations, and the agreement between experimental and predicted results was in general found to be good.
The deformation behaviour of polyoxymethylene has been studied in plane strain compression at temperatures from 120 °C up to 165 °C and in uniaxial tension and simple shear at 160 °C for strain rates from 10−4 to 1 s−1. In uniaxial tension the stress–strain behaviour was determined by a novel video-controlled testing system. The measurements showed that there was a very significant evolution of volumetric strain, indicating that damage mechanisms play a key role in the plastic deformation behaviour.All tests showed similar deformation stages with a short region of visco-elastic behaviour followed by a rounded yield point. The von Mises equivalent yield stress for these tests showed a linear relationship with logarithmic strain rate, suggestive of an Eyring type thermally activated process. After yielding, all stress–strain curves showed a long plastic deformation regime, which in shear occurred at constant stress. In plane strain compression there was also only a very small increase in stress, in contrast to uniaxial tension where very significant strain hardening was observed at high strains, which is attributed to the onset of structural changes.
An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation
attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation
coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and
Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical
properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum
alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends
of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated.
This paper presents an experimental and numerical investigation on low velocity perforation (in the velocity range 3.5–15.8 m/s) of AA5083-H116 aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical blunt-nosed projectile. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA in order to investigate the effects of anisotropy, dynamic strain aging (causing negative strain rate sensitivity) and thermal softening in low velocity impacts on the present aluminium alloy. Dynamic strain aging has been shown to influence both the predicted force level and fracture, while thermal softening only influences fracture prediction. No significant effect of plastic anisotropy has been observed.
A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10−5 to 5000 s−1) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.
The plugging capacity of simply supported and continuous plates in steel grade St 52-3N, subjected to a dropped drill-collar in the velocity range frame 0–50 m s−1 has been studied experimentally. All tests have been carried out in scale 1:4 and the target thickness, inplane stiffness of target, and mass of the projectile have been the primary variables. In addition to the dynamic tests, static punch tests have been carried out to study any relationship between the dynamic and static plugging capacities.
The intention of this paper is to give a comparative review of material models for polymers with special focus on crashworthiness analysis. An outline of polymers classified as incompressible elastomers, compressible foams and thermoplastics is shown. Elastomers and recoverable foams are based on the same theoretical description: hyperelasticity. We present a material law that allows fast generation of input data based on uniaxial static and dynamic tensile tests at different strain rates. For thermoplastics, we give a short overview of suitable material laws and show how we can characterize approximately their behaviour by using metal plasticity. Using pedestrian protection as an example, we demonstrate some typical applications of polymer modelling in crash simulation. Furthermore, we investigate the deformation behaviour of a Hardy disk during a frontal offset impact.
Classical models based on the thermodynamics of irreversible process with internal variables dedicated to the inelastic analysis of metallic structures are modified and then used for modeling the mechanical behavior of polymers. The major difference comes from the expression of the yield criterion. Indeed, a generalized yield criterion, based on the parabolic Drucker and Prager criterion, is proposed including the first invariant of the stress tensor as well as the second invariant and the third invariant of the deviatoric part of the stress tensor. Close agreement between experimental data and yielding predictions is obtained for various polymers loaded under different states of stress. It has been established that the temperature T, the strain rate , the critical molecular mass Mc and the degree of crystallinity Xc do not affect the parameter m of the proposed yield function. Furthermore, viscoplastic constitutive equations are developed in the framework of the general principles of thermodynamics with internal variables for generalized materials considering only the kinematic hardening rule. Experimental data obtained under different loading conditions are well reproduced by the proposed model. An accurate identification of the model parameters and the introduction of the isotropic hardening variable into the yield function and the drag stress will improve the predictions of the overall mechanical behavior of polymers especially the unloading path.
This paper presents an original three dimensional (3D) analytical general solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar and its applications to some experimental methods of material behaviour testing to improve their accuracy. One application is to take into account the wave dispersion effects in the split Hopkinson pressure bar (SHPB) setup composed of viscoelastic bars. Another is to eliminate the geometrical effects in an impulse test in which the linear viscoelastic material properties can be deduced from the change in the wave shape due to the propagation between two points of measurement in a specimen bar.
Polycarbonate is a polymer which is used for lightweight transparent armour in a wide range of applications. The material has an unusually high yield strain and ductility; this combined with a significant amount of strain hardening enables it to display impressive impact and perforation resistance. In this paper experimental observations are reported of penetration and perforation of polycarbonate plates by ballistic impact. Five mechanisms of deformation and subsequent fracture of the plate are identified. They are: elastic dishing, petalling, deep penetration, cone cracking and plugging. Thin plates impacted by spherical missiles exhibit elastic dishing, whereas thick plates suffer a deep penetration process. In both cases, final failure is by petalling. Cylindrical missiles impacting thick plates also cause deep penetration with final failure occurring by plugging. For thin plates impacted by cylindrical missiles, cone cracking develops from the leading edge of the missile. These process are described in detail, and the regime for each mechanism of failure is identified.
The use of finite element methods is described for predicting the deformation of a tough thermoplastic material under different loading speeds including impact. An elastic-plastic model is used in the simulation for describing the large-strain, non-linear behaviour of the polymer. The determination of the materials, properties and parameters required by the model, and their dependence upon strain rate, is described. Some limitations in the use of this model for plastics are illustrated through the analysis of results from an ABS polymer.Predictions are made for the deformation of a circular plate of the ABS polymer that is supported by a circular ring and loaded at its centre by a rigid hemispherical surface. Predicted results are compared with measurements of force against central deflection at different speeds up to 1 m/s. Comparisons are also made at a lower speed between measured and predicted strains around the centre of the plate.
Most materials, especially polymers, can, after exposure to environmental agents, degrade by chemical and physical processes and have their performance modified. The rate of degradation, slow or fast, which depends on the kind of agent, will influence the useful lifetime of the material. The increased use of the polymers in ballistic armor and the insufficient information about the influence of environmental degradation on the dynamic behavior show the need of additional studies. In the present work, using exposition to gamma radiation to accelerate degradation, the mechanical and ballistic behavior of a transparent laminate armor manufactured with polycarbonate plates was studied. The results are presented and discussed.
Il is a pressing objective to understand the mechanical behaviour of polymeric materiais at high strain rate for a range of industrial and defence applications. Some are used as the binder phase in plastic bonded explosives (PBXs) and propellants. Others are used either as components for structures or as the binder phase in various composite Systems. Such materials need to be understood so that their response may be understood and constitutive descriptions constructed. This work presents experimental data focused at the evaluation of the equation-of-statc (EOS) and strength behaviour of four selected polymers. The equation of state and the shear strength of each polymer were measured as a function of impact stress and this gives insight into the role of the microstructure and its relation to response.
Principles of polymer engineering
- Mccrum Ng
- Buckley Cp
- Cb
McCrum NG, Buckley CP, Bucknall CB. Principles of polymer engineering. Oxford Science Publications; 1997.
Comparison of transverse deformation field found from optical full-field measurements and numerical predictions for a 5 mm thick PVC plate subjected to a 6
- Fig
Fig. 27. Comparison of transverse deformation field found from optical full-field measurements and numerical predictions for a 5 mm thick PVC plate subjected to a 6.9 m/s impact.
Low energy impact evaluation using non conservative models
- O Jimé Nez
- J A Sullcahuaman
- M Sá Nchez-Soto
- A B Martinez
Jimé nez O, Sullcahuaman JA, Sá nchez-Soto M, Martinez AB. Low energy
impact evaluation using non conservative models. Int J Solids Struct
2006;42:5758-64.
Principles of polymer engineering
- N G Mccrum
- C P Buckley
- C B Bucknall
McCrum NG, Buckley CP, Bucknall CB. Principles of polymer engineering.
Oxford Science Publications; 1997.
LS-DYNA keyword user's manual. Version 971. Livermore Software Technology Corporation
- Ls-Dyna
LS-DYNA. LS-DYNA keyword user's manual. Version 971. Livermore Software
Technology Corporation; 2007.