Mechanics of Materials

Published by Elsevier
Print ISSN: 0167-6636
Ultrasound waves have a broad range of clinical applications as a non-destructive testing approach in imaging and in the diagnoses of medical conditions. Generally, biological tissues are modeled as an homogenized equivalent medium with an apparent density through which a single wave propagates. Only the first wave arriving at the ultrasound probe is used for the measurement of the speed of sound. However, the existence of a second wave in tissues such as cancellous bone has been reported and its existence is an unequivocal signature of Biot type poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as density, a fabric-dependent anisotropic poroelastic ultrasound (PEU) propagation theory was recently developed. Key to this development was the inclusion of the fabric tensor - a quantitative stereological measure of the degree of structural anisotropy of bone - into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of waves in several soft and hard tissues. It was found that collagen fibers in soft tissues and the mineralized matrix in hard tissues are responsible for the anisotropy of the solid tissue constituent through the fabric tensor in the model.
The annulus fibrosus (AF) of the intervertebral disc experiences cyclic tensile loading in vivo at various states of mechanical equilibrium. Disc degeneration is associated with alterations in the biochemical composition of the AF including decreased water content, decreased proteoglycan concentration, and increased collagen deposition that affect mechanical function of the AF in compression and shear. Such changes may also affect the dynamic viscoelastic properties of the AF and thus alter the disc's ability to dissipate energy under physiologic loading. The objectives of this study were to quantify the dynamic viscoelastic properties of human AF in circumferential tension and to determine the effect of degeneration on these properties. Nondegenerated and degenerated human AF tensile samples were tested in uniaxial tension over a spectrum of loading frequencies spanning 0.01Hz to 2Hz at several states of equilibrium strain to determine the dynamic viscoelastic properties (dynamic modulus, phase angle) using a linear viscoelastic model. The AF dynamic modulus increased at higher equilibrium strain levels. The AF behaved more elastically at higher frequencies with a decreased phase angle. Degeneration resulted in a higher dynamic modulus at all strain levels but had no effect on phase angle. The findings from this study elucidate the effect of degeneration on the dynamic viscoelastic properties of human AF and lend insight into the mechanical role of the AF in cyclic loading conditions.
Explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity (the well-known open interface crack model is employed for the solution). Since the interfacial spring stiffness can be experimentally determined from ultrasound reflection and transmission analysis, the proposed expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting (independent) cracks and the crack interaction factor. In order to avoid the effect of the crack surface interpenetration zones on the effective spring stiffness, the range of the tensile to transverse load ratios is obtained under the assumption of small-scale contact conditions. Since real cracks are often slightly open (due to prior loading history and plastic deformation), it is demonstrated that for ultrasound applications the results obtained are valid for most practical cases of small interfacial cracks as long as the mid-crack opening normalized by the crack length is at least in the order of 10(-5).
Adaptations of large arteries to sustained alterations in hemodynamics that cause changes in both caliber and stiffness are increasingly recognized as important initiators or indicators of cardiovascular risk to high flow, low resistance organs such as the brain, heart, and kidney. There is, therefore, a pressing need to understand better the underlying causes of geometric and material adaptations by large arteries and the associated time courses. Although such information must ultimately come from well designed experiments, mathematical models will continue to play a vital role in the design of these experiments and their interpretation. In this paper, we present a new multilayered model of the time course of basilar artery growth and remodeling in response to sustained alterations in blood pressure and flow. We show, for example, that single- and multi-layered models consistently predict similar changes in caliber and wall thickness, but multilayered models provide additional insight into other important metrics such as the residual stress related opening angle and the axial prestress, both of which are fundamental to arterial homeostasis and responses to injury or insult.
The attachment of tendon to bone, one of the greatest interfacial material mismatches in nature, presents an anomaly from the perspective of interfacial engineering. Deleterious stress concentrations arising at bi-material interfaces can be reduced in engineering practice by smooth interpolation of composition, microstructure, and mechanical properties. However, following normal development, the rotator cuff tendon-to-bone "insertion site" presents an interfacial zone that is more compliant than either tendon or bone. This compliant zone is not regenerated following healing, and its absence may account for the poor outcomes observed following both natural and post-surgical healing of insertion sites such as those at the rotator cuff of the shoulder. Here, we present results of numerical simulations which provide a rationale for such a seemingly illogical yet effective interfacial system. Through numerical optimization of a mathematical model of an insertion site, we show that stress concentrations can be reduced by a biomimetic grading of material properties. Our results suggest a new approach to functional grading for minimization of stress concentrations at interfaces.
Carbon Nanotube/High Density Polyethylene (CNT/HDPE) composites were manufactured and tested to determine their wear behavior. The nanocomposites were made from untreated multi-walled carbon nanotubes and HDPE pellets. Thin films of the precursor materials were created with varying weight percentages of nanotubes (1%, 3%, and 5%), through a process of mixing and extruding. The precursor composites were then molded and machined to create test specimens for mechanical and wear tests. These included small punch testing to compare stiffness, maximum load and work-to-failure and block-on-ring testing to determine wear behavior. Each of the tests was conducted for the different weight percentages of composite as well as pure HDPE as the baseline. The measured mechanical properties and wear resistance of the composite materials increased with increasing nanotube content in the range studied.
Recent work has demonstrated that enzymatic degradation of collagen fibers exhibits strain-dependent kinetics. Conceptualizing how the strain dependence affects remodeling of collagenous tissues is vital to our understanding of collagen management in native and bioengineered tissues. As a first step towards this goal, the current study puts forward a multiscale model for enzymatic degradation and remodeling of collagen networks for two sample geometries we routinely use in experiments as model tissues. The multiscale model, driven by microstructural data from an enzymatic decay experiment, includes an exponential strain-dependent kinetic relation for degradation and constant growth. For a dogbone sample under uniaxial load, the model predicted that the distribution of fiber diameters would spread over the course of degradation because of variation in individual fiber load. In a cross-shaped sample, the central region, which experiences smaller, more isotropic loads, showed more decay and less spread in fiber diameter compared to the arms. There was also a slight shift in average orientation in different regions of the cruciform.
Glaucoma is among the leading causes of blindness worldwide. The ocular disease is characterized by irreversible damage of the retinal ganglion cell axons at the level of the lamina cribrosa (LC). The LC is a porous, connective tissue structure whose function is believed to provide mechanical support to the axons as they exit the eye on their path from the retina to the brain. Early experimental glaucoma studies have shown that the LC remodels into a thicker, more posterior structure which incorporates more connective tissue after intraocular pressure (IOP) elevation. The process by which this occurs is unknown. Here we present a microstructure motivated growth and remodeling (G&R) formulation to explore a potential mechanism of these structural changes. We hypothesize that the mechanical strain experienced by the collagen fibrils in the LC stimulates the G&R response at the micro-scale. The proposed G&R algorithm controls collagen fibril synthesis/degradation and adapts the residual strains between collagen fibrils and the surrounding tissue to achieve biomechanical homeostasis. The G&R algorithm was applied to a generic finite element model of the human eye subjected to normal and elevated IOP. The G&R simulation underscores the biomechanical need for a LC at normal IOP. The numerical results suggest that IOP elevation leads to LC thickening due to an increase in collagen fibril mass, which is in good agreement with experimental observations in early glaucoma monkey eyes. This is the first study to demonstrate that a biomechanically-driven G&R mechanism can lead to the LC thickening observed in early experimental glaucoma.
The six-dimensional orthogonal tensor representation of the rotation about an axis in three dimensions was first proposed by Mehrabadi et al. [Mehrabadi, M.M., Cowin, S.C., Jaric, J., 1995. Six-dimensional orthogonal tensor representation of the rotation about an axis in three dimensions. International Journal of Solids and Structures 32 (3-4), 439-449]. In this brief note, a simple and coherent approach is presented to construct the six-dimensional orthogonal tensor representation of the rotation of any parametrization in three dimensions and to prove its orthogonality.
The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori-Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller's octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75-90% of the total variance. An implementation of the proposed methods was made publicly available.
This contribution presents an alternative approach to mixture theory-based poroelasticity by transferring some poroelastic concepts developed by Maurice Biot to mixture theory. These concepts are a larger RVE and the subRVE-RVE velocity average tensor, which Biot called the micro-macro velocity average tensor. This velocity average tensor is assumed here to depend upon the pore structure fabric. The formulation of mixture theory presented is directed toward the modeling of interstitial growth, that is to say changing mass and changing density of an organism. Traditional mixture theory considers constituents to be open systems, but the entire mixture is a closed system. In this development the mixture is also considered to be an open system as an alternative method of modeling growth. Growth is slow and accelerations are neglected in the applications. The velocity of a solid constituent is employed as the main reference velocity in preference to the mean velocity concept from the original formulation of mixture theory. The standard development of statements of the conservation principles and entropy inequality employed in mixture theory are modified to account for these kinematic changes and to allow for supplies of mass, momentum and energy to each constituent and to the mixture as a whole. The objective is to establish a basis for the development of constitutive equations for growth of tissues.
This paper presents the results of a combined experimental and analytical study of fatigue crack growth and dwell-fatigue crack growth in forged Ti–6Al–2Sn–4Zr–2Mo–0.2%Si (Ti-6242). Following an initial characterization of microstructures and basic mechanical properties, the micromechanisms of long fatigue crack growth are presented for three microstructures. These include: a duplex α/β structure, an elongated α/β structure, and a colony α/β microstructure. The colony microstructure is shown to have the best resistance to fatigue crack growth. The elongated α structure has intermediate resistance, while the equiaxed α structure exhibits the fastest fatigue crack growth rates. The fatigue crack growth rates in the near-threshold, Paris and high ΔK regimes are then characterized with empirical crack growth laws that relate the crack growth rates to the stress intensity factor range and key parameters on the fatigue crack growth curve. Finally, the results of dwell-fatigue crack growth experiments are presented for the three microstructures. The dwell-fatigue crack growth rates are shown to be almost identical to the fatigue crack growth rates in the intermediate ΔK regime. However, the fatigue crack growth rates are faster at higher stress intensity factor ranges. The underlying mechanisms of dwell crack growth are compared with the mechanisms of fatigue crack growth before discussing the implications of the work for the prediction of dwell or fatigue crack growth in Ti-6242. The effects of cyclic frequency on fatigue crack growth are also explored.
Two-and three-dimensional models, both containing 10 grains.  
Constant k for different load cases in two and three dimensions
A numerical model based on the finite element method is presented for modeling of microstructures. The model uses a discrete version of the Voronoi algorithm to partition the mesh into grains. The model is utilized to study representativity of grain structures. The number of grains needed in a representative volume element is evaluated for materials with cubic symmetry and random texture. It is shown that the number of grains needed depend on the anisotropy, and a simple expression that relates anisotropy and the number of grains is suggested.
This paper summarizes the results of a recent breakthrough in explicit constitutive computational algorithms for finite-element calculations of large-deformation rate-independent elastoplasticity, using the example of the J2 yield condition and flow rule with isotropic hardening. The new algorithm provides a direct, explicit, and always nearly exact estimate of the yield surface and all stress components, for any prescribed deformation increment (large or small) in one single step with no iterations, or in any desired number of substeps. The algorithm does not depend on radial return, and can accommodate nonsmooth yield surfaces. This generalization is also briefly discussed.
Atomistic simulations are performed for the study of defect nucleation and evolution in Al single crystal under nanoindentation. Methodologies employed include the molecular dynamics and molecular mechanics simulations with embedded-atom potentials. Simulated is the indenting process on Al(1 1 1) surface with the spherical tip of indenter. Using the visualization technique of centrosymmetry parameters, homogeneous nucleations and early evolutions of dislocations are investigated for deepening our understanding of incipient plasticity at the atomic scale. We have shown that the nucleation sites of initial dislocation loops vary with the empirical potentials chosen for the simulation. Identifications are also made for the continuously changing structures of dislocation locks underneath the indenter tip and for the glide of prismatic partial dislocation loops far away from the contact surface.
The cyclic deformation behavior of HAYNES® HR-120® superalloy at different temperatures ranging from 24 to 982 °C was investigated by performing fully reversed total strain-controlled low-cycle fatigue tests under the total strain ranges of 0.4–2.3%. It was noted that in most cases, increasing the temperature from 24 to 982 °C significantly decreased the fatigue lives. The alloy exhibited the cyclic hardening, softening, or stable cyclic stress response, which was dependent on the temperature and total strain range. Dynamic-strain aging was found to occur at both temperatures of 761 and 871 °C. The precipitation of secondary-phase particles was also observed above 761°C. The change in the microstructure due to cyclic deformation was evaluated through scanning electron microscopy and transmission electron microscopy. In addition, an advanced infrared thermography system was employed to monitor the temperature evolution during fatigue at 24 °C. It was noted that during low-cycle fatigue, the steady-state temperature of the specimens increased from 2 to 120 °C above room temperature, depending on the strain range and fatigue life. Thus, the measured temperature can be used to predict fatigue life. A model based on energy conservation and one-dimensional heat conduction was used to predict the temperature evolution resulting from low-cycle fatigue.
Motivated by eventual applications as high temperature actuators, cyclic isothermal stress-induced transformations of Cu–13.3Al–4.0Ni (wt.%) single crystal wires with stress-free transformation temperatures: Mf = 80 °C, Ms = 100.5 °C, As = 104.5 °C and Af = 117 °C were studied under the two adverse conditions of high overall strain (9%) and an overheating temperature (175 °C for 30 min). Wires were subjected to isothermal stress cycling at 25 °C using an Instron testing machine with environmental chamber until fairly repetitive stress–strain response was obtained. These tests were repeated on the same specimen at progressively higher temperatures of 40, 60, 80 and 100 °C. It is seen that the initial cyclic response is primarily shape memory whereas the subsequent cyclic response is primarily pseudoelastic, attended by some residual inelastic deformation. Tests on a different virgin specimen at 100, 120, 140 and 160 °C showed a similar trend. This points to the possibility of a downward shift in the stress-free transformation temperatures. Possible reasons are generation of dislocations as well as the domination of α-martensites over β-martensites due to the overheating temperature and stress cycling. The effect of stress cycles on overall strain on full loading, after unloading and after heating in between stress cycles has been discussed.
An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cement's stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.
A method is developed herein for predicting the life of a continuous fiber titanium metal matrix composite. As a part of the research effort, the titanium metal matrix composite, SCS-6/Timetal®21S [0]4, has been fatigue tested at 482°C and 650°C. Additional specimens have been environmentally degraded at 700°C and then fatigued at 482°C to failure. The research focuses on initial oxygen dissolution and its effect on the life of the material. The life-limiting physical mechanisms identified from the experiments are material inelasticity, surface embrittlement, and subsequent surface cracking, fiber/matrix debonding, fiber-bridging, and eventual fiber failure. A model incorporating all of these physical phenomena has been developed herein. The model utilizes the finite element method coupled with models for material inelasticity, surface embrittlement, and crack propagation. Material inelasticity is predicted using Bodner's unified viscoplastic model. Crack propagation is modelled via the inclusion of cohesive zones. Surface embrittlement is accounted for by degrading material properties. Both monotonic and fatigue loadings have been modelled at 482°C and 650°C for degraded and undegraded specimens. Results indicate that surface crack propagation rates are significantly slower when matrix viscoplasticity is included in the model instead of elasticity. Furthermore, surface cracking in environmentally degraded specimens enhances fiber stresses compared to undegraded specimens. This difference apparently leads to the premature failure of the degraded composite.
An effort is made to predict the crack growth of the stainless steel 304L based on a newly developed fatigue approach. The approach consists of two steps: (1) elastic–plastic finite element (FE) analysis of the component; and, (2) the application of a multiaxial fatigue criterion for the crack initiation and growth predictions based on the outputted stress–strain response from the FE analysis. The FE analysis is characterized by the implementation of an advanced cyclic plasticity theory that captures the important cyclic plasticity behavior of the material under the general loading conditions. The fatigue approach is based upon the notion that a material point fails when the accumulated fatigue damage reaches a certain value and the rule is applicable for both crack initiation and growth. As a result, one set of material constants is used for both crack initiation and growth predictions. All the material constants are generated by testing smooth specimens. The approach is applied to Mode I crack growth of compact specimens subjected to constant amplitude loading with different R-ratios and two-step high–low sequence loading. The results show that the approach can properly model the experimentally observed crack growth behavior including the notch effect, the R-ratio effect, and the sequence loading effect. In addition, the early crack growth from a notch and the total fatigue life can be simulated with the approach and the predictions agree well with the experimental observations.
A physical based model for the evolution of flow stress of AISI 316L from room temperature up to 1300 °C, strains up to 0.6 and strain rates from 0.0005 up to 10 s−1 is developed. One set of tests have been used for model calibration and another more complex set of tests for its validation. The model is based on a coupled set of evolution equations for dislocation density and (mono) vacancy concentration. Furthermore, it includes the effect of diffusing solutes in order to describe dynamic strain ageing (DSA). The model described the overall flow stress evolution well with exception of the details of the effect of the DSA phenomenon. Its numerical solution is implemented in a format suitable for large-scale finite element simulations.
In this paper, a viscoplastic model incorporated with the hardening caused by the combined monotonic and cyclic strain loading is proposed. It is assumed that the isotropic and kinematic hardening rules are dependent on both the cyclic inelastic strain amplitude and the maximum inelastic strain. The current inelastic strain amplitude is described by a memory model in which the current inelastic strain amplitude can be approached very quickly. The fading memory on the previous maximum deformation resistance is taken into account to describe the fading memory on the previous loading history while the deformation resistance is presented by both the maximum inelastic strain and the current inelastic strain amplitude. The comparison between the predicted and experimental results indicated that the model can describe the ratcheting behavior under uniaxial cyclic stressing and the cyclic strain behavior under uniaxial cyclic straining in the unified viscoplastic model.
The stress–strain behavior of elastomeric materials is known to be rate-dependent and to exhibit hysteresis upon cyclic loading. Although these features of the rubbery constitutive response are well-recognized and important to its function, few models attempt to quantify these aspects of response. Experiments have acted to isolate the time-dependent and long term equilibrium components of the stress–strain behavior (Bergström, J.S., Boyce, M.C., 1998. J. Mech. Phys. Solids 46, 931–954). These data formed the foundation of a constitutive model for the time-dependent, hysteretic stress–strain behavior of elastomers where the behavior is decomposed into an equilibrium molecular network acting in parallel with a rate-dependent network (cf. loc. cit.). In this paper, the Bergstrom and Boyce constitutive model is extended to specifically account for the effect of filler particles such as carbon black on the time-dependent, hysteretic stress–strain behavior. The influence of filler particles is found to be well-modeled by amplification of scalar equivalent values of the stretch and the shear stress thus providing effective measures of matrix stretch and matrix shear stress. The amplification factor is dependent on the volume fraction and distribution of filler particles; three-dimensional stochastic micromechanical models are presented and verify the proposed amplification of stretch and stress. A direct comparison between the new model and experimental data for two series of filled elastomers (a chloroprene rubber series and a natural rubber series) indicates that the new model framework successfully captures the observed behavior. The success of the model implies that the effects of filler particles on the equilibrium, rate and hysteresis behavior of elastomers mainly requires a treatment of the composite nature of the microstructure and not micro-level concepts such as alteration of mobility or effective crosslinking density of the elastomeric phase of the material.
This paper describes a method to design the periodic microstructure of a material to obtain prescribed constitutive properties. The microstructure is modelled as a truss or thin frame structure in 2 and 3 dimensions. The problem of finding the simplest possible microstructure with the prescribed elastic properties can be called an inverse homogenization problem, and is formulated as an optimization problem of finding a microstructure with the lowest possible weight which fulfils the specified behavioral requirements. A full ground structure known from topology optimization of trusses is used as starting guess for the optimization algorithm. This implies that the optimal microstructure of a base cell is found from a truss or frame structure with 120 possible members in the 2-dimensional case and 2016 possible members in the 3-dimensional case. The material parameters are found by a numerical homogenization method, using Finite-Elements to model the representative base cell, and the optimization problem is solved by an optimality criteria method.Numerical examples in two and three dimensions show that it is possible to design materials with many different properties using base cells modelled as truss or frame works. Hereunder is shown that it is possible to tailor extreme materials, such as isotropic materials with Poisson's ratio close to − 1, 0 and 0.5, by the proposed method. Some of the proposed materials have been tested as macro models which demonstrate the expected behaviour.
To understand and model the thermomechanical response of DH-36 Naval structural steel, uniaxial compression tests are performed on cylindrical samples, using an Instron servohydraulic testing machine and UCSD’s enhanced Hopkinson technique. True strains exceeding 60% are achieved in these tests, over the range of strain rates from 0.001/s to about 8000/s, and at initial temperatures from 77 to 1000 K. The microstructure of the undeformed and deformed samples is examined through optical microscopy. The experimental results show: (1) DH-36 steel displays good ductility and plasticity (strain > 60%) at low temperatures (even at 77 K) and high strain rates; (2) at relatively high temperatures and low strain rates (especially below about 0.1/s), its strength is not temperature sensitive, indicating that the material has good weldability; (3) dynamic strain aging (DSA) occurs at temperatures between 500 and 1000 K and in the range of strain rates from 0.001/s to 3000/s, the peak value of the stress shifting to higher temperatures with increasing strain rates (it is about 600 K at 0.001/s, about 650 K at 0.1/s, and about 800 K at 3000/s); (4) adiabatic shearbands develop when the strain exceeds about 30% at 77 K, and at higher strains for higher temperatures; and (5) the microstructural evolution of the material is not very sensitive to changes in strain rates and temperatures. Finally, based on the mechanism of dislocation motion, and using our experimental data, the parameters of a physically-based model developed earlier for AL-6XN stainless steel [J. Mech. Phys. Solids 49 (2001) 1823] are estimated and the model predictions are compared with various experimental results, excluding the dynamic strain aging effects. Good agreement between the theoretical predictions and experimental results is obtained. In order to further verify the model independently of the experiments used in the modeling, additional compression tests at a strain rate of 8000/s and various initial temperatures are performed, and the results are compared with the model predictions. Good correlation is observed. As an alternative to this model, the experimental data are also used to estimate the parameters in the Johnson–Cook model [G.R. Johnson, W.H. Cook, 1983, in: Proceedings of the Seventh International Symposium on Ballistic, The Hague, The Netherlands, p. 541] and the resulting model predictions are compared with the experimental data, again excluding the dynamic strain-aging effects. These and related results suggest that the physically based model has a better prediction capability over a broader strain rate and temperature range.
Numerical and experimental studies on the impact and penetration of armor plates subjected to sub-ordnance range impact velocities by pointed and flat strikers is presented. Three target scenarios are considered: (1) a blank (unbacked) steel plate; (2) the same steel plate backed by a thick layer of polyurea; and (3) two identical steel plates of half the original thickness placed on both sides of the polyurea layer. For the blank plate, two fracture mechanisms of the steel plate – shear plugging and petalling of the plates – are observed in the simulation. For the same plate with a thick polyurea coating at the back side, it is found that the polyurea coating provides additional resistance in terms of energy absorption through two mechanisms: (1) the increase in the energy dissipated by the steel plate and (2) increased energy stored in the polyurea itself. For the sandwich configuration of the target plate, where the polyurea layer is placed between two steel plates, no advantage in terms of penetration resistance is found. These numerical results agree with experimental observations on the failure modes and exit velocities.
A representation of anisotropic poroelasticity is derived in which the drained and undrained elastic compliance constants, as well as the permeability tensor, are expressed as functions of the fabric tensor. The fabric tensor employed is a quantitative stereological measure of the anisotropy of the structure of the pores in the porous medium. It is shown that the undrained elastic constants may be expressed as functions of the fabric tensor, the drained elastic constants, the porosity, the bulk moduli of the fluid and the matrix material.
In this paper, a damage-coupled unified visco-plastic constitutive model is proposed for 63Sn–37Pb alloy used in solder joints of surface-mount IC packages and semiconductor devices that are subjected to mechanical fatigue loading at two constant high temperatures. The model accounts for the time and temperature dependence of the kinematic hardening, and is represented by the back stress state variable which evolves according to the hardening-recovery equations with different evolution rates. The damage evolution equation, including cyclic plastic damage and time-dependent cyclic damage, is established, and a failure criterion is proposed based on the damage accumulation in materials. The model is used to predict the effects of strain rates, temperature and dwell time on both the deformation and fatigue life of 63Sn–37Pb solder alloy under cyclic straining with and without dwell time at two temperatures.
A stress–magnetic field–temperature phase diagram of polycrystalline Fe–30.5%Pd ferromagnetic shape memory alloy (FSMA) is constructed based on experimental results and a thermodynamic model. The 3D-phase transformation diagram provides a key performance map in guiding us which actuation mechanism is the best for a given FSMA. According to this 3D-phase transformation diagram, the magnetic field induced transformation is found to be insignificant, while the hybrid mechanism based on the stress-induced martensitic transformation induced by the magnetic field gradient is more attractive. The NiMnGa system is also examined.
In this paper, three-dimensional beam lattice models are extended and used for simulating size effects on strength of 3-point bending fracture experiments on concrete. At the meso-level concrete is schematized as a three-phase material, consisting of aggregate particles, cement matrix and the bond zone, which separates these two phases. Displacement-controlled 3-point bending experiments are simulated varying the particle density Pk (Pk = 0%, 15%, 35% and 55%) and the specimen size, which is scaled in all three dimensions in a range of 1:8 (volume range 1:512), containing between 15,703 and 7,448,373 lattice elements. The numerical analyses show particle density dependent scaling behaviour of strength. For very low (0%) and high (55%) particle density, scaling comes close to classical Weibull theory; for intermediate densities a significantly different power emerges caused by stable pre-critical crack growth leading to hardening.
Porous materials due to their complex geometry are difficult to be examined by FEM-based approaches and usually are simulated by simplified geometrical models. In the present paper a novel procedure for describing the solid geometry of open-cell foams is introduced, facilitating the establishment of a corresponding FEM model for simulating the material behavior in micro-tension. Open-cell Al-foams were fabricated using the polymer impregnating method. A serial sectioning image-based process is described to capture, reproduce and visualize the exact three-dimensional (3D) microstructure of the examined foam. The generated 3D geometry of the Al-foam, derived from the synthesis of digital cross sectional images of the foam, was appropriately adjusted to build a FE model simulating the deformation conditions of the Al-foam under micro-tension loads. The obtained results render possible the visualisation of the stress fields in the Al-foam, allowing for a full investigation of its mechanical behavior.
In the first part of this paper, a uniaxial nonlinear viscoelastic model has been established to describe the long-term creep behaviour of an unsaturated polyester resin. The model was based on Schapery's thermodynamics-based theory, and included effects of physical ageing. In the present (second) part, this model is extended into a general three-dimensional form. In the 3D-model a creep contraction ratio and an instantaneous elastic Poisson's ratio are introduced. By assuming both ratios constant, albeit different from each other for all load levels, a model is obtained which is able to describe the experimentally obtained creep-recovery curves very well. A numerical scheme for the developed constitutive equations is then established and the 3D theory is implemented into a finite element method (FEW package. In addition tests have been carried out in order to verify the theory. Tensile creep tests performed on plate-shaped specimen with a central circular hole were used to check the model calculations. In such a test plate a two-dimensional stress state exists close to the hole. Also creep and relaxation processes occur simultaneously during the test. A further validation of the model was carried out by loading unsaturated polyester thin-walled tubes under a combined tension-torsion loading. The comparison between the experimental data and the FEM calculations shows a good agreement. The good agreement obtained under biaxial stress fields leads to the conclusion that the uniaxial creep-recovery tests characterized model can be used to describe three-dimensional loading situations satisfactorily.
This paper concerns the mechanical behavior of super-elastic polycrystalline shape memory alloys under cyclic loadings. Sometimes, as shown by many experimental observations, a permanent inelastic strain occurs and increases with the number of cycles. A series of cyclic tests has been carried out and used to develop a 3D macroscopic model for the super-elasticity of SMAs able to describe the evolution of permanent inelastic strain during cycles.
Experiments have been conducted to investigate the process by which adiabatic shear bands are formed in an AISI 4340 VAR steel with HRC = 44. To produce the shear bands, short, thin-walled tubular specimens were deformed in torsion at a nominal shear strain rate of about 103 s−1 in a Kolsky bar apparatus (split-Hopkinson bar). Strains of a few hundred percent and local strain rates of 105 s−1 were reached in the region of localization. The temperature rise in the band, recorded using an infra-red detector, was approximately 460°C. Microscopic observations of deformed samples were made by transmission electron microscopy (TEM). The TEM observations revealed that the material within the shear band was characterized by highly elongated subgrains and dislocation cells. The subgrain boundaries were generally well-defined and the subgrains varied in dislocation density. To elucidate the softening mechanism, the misorientations between subgrains and dislocation cells were measured. There was no indication of a phase transformation within the shear band. The probable metallurgical processes involved in shear band formation are presented in light of these experimental results.
This paper presents the results of a systematic comparative study of the dynamic thermomechanical response of Ti–6Al–4V alloys with three different microstructures. Two of the alloys are produced by the hot isostatically pressed technique using rapidly solidified granules, with one alloy milled prior to hot pressing. Experiments are performed over a broad range of strain rates, 10−3–, and initial temperatures, 77–1000 K. Depending on the test temperature, compressive strains of 10–60% are achieved. The microstructure of the undeformed and deformed specimens is investigated, using optical microscopy. The dependence of the flow stress on the temperature and the strain rate is examined for various strains and it is related to the corresponding material microstructure. The results show that adiabatic shearbands develop at high strain rates, as well as at low strain rates and high temperatures. Depending on the test temperature, shearbands initiate once a sample is deformed to suitably large strains. The flow stress is more sensitive to temperature than to the strain rate. Based on these results and other published work, the thermally activated mechanisms associated with the dislocation motion are identified. The physically based model proposed by Nemat-Nasser and Li (1997) for OFHC copper, is suitably modified and applied to this class of titanium alloys. In the absence of dynamic strain aging, the model predictions are in good accord with the experimental results. Comparing the results for the three considered Ti–6Al–4V alloys, with different microstructures, it is found that the initial microstructural features affect only the magnitude of the threshold stress and the athermal part of the flow stress, but not the functional dependence of the thermally activated part of the flow stress on the temperature and the strain rate.
This paper presents the results of an experimental study of fatigue crack nucleation and growth in a Ti–6Al–4V/TiB in situ whisker-reinforced composite. The onset of crack nucleation is shown to correspond to ∼20% of the total life at a stress range of 480 MPa. This is associated with transverse cracking across TiB whiskers, and interfacial decohesion between the TiB whiskers and the Ti–6Al–4V matrix. Subsequent cracking occurs by the formation of multiple cracks across the elongated α grains. These cracks are retarded initially by the β phase. However, subsequent fatigue damage results in transgranular crack growth across α and β phases prior to the onset of catastrophic failure. The long fatigue crack growth rates in the Paris regime in the Ti–6Al–4V/TiB composite are comparable to those of Ti–6Al–4V processed under nominally identical conditions. However, the fatigue crack growth rates in the composite are faster than those in the matrix alloy at lower ΔK values. Cyclic deformation of the composite is associated with strain softening, presumably as a result of progressive interfacial decohesion around the TiB whiskers early in the fatigue deformation process. The implications of the results are assessed for potential structural applications of the Ti–6Al–4V/TiB composite.
The effect of initial plastic strain on the high cycle fatigue (HCF) lives of smooth cylindrical Ti–6Al–4V specimens is investigated. Specimens were monotonically, quasi-statically loaded under strain control in tension to produce plastic strains from 1% to 5% and under load control in compression to produce 9.5% plastic strain. A step-loading technique was then employed to establish the 106 or 107 cycle fatigue limit stress under load control conditions for stress ratios of R=0.1, 0.5 and 0.8 at frequencies of either f=50 or 400 Hz. Results are compared with baseline fatigue limit stresses for Ti–6Al–4V without prior plastic strain. Initial plastic prestrain in both tension and compression resulted in a small reduction in the fatigue limit at R=0.1, while a lesser reduction was exhibited at higher stress ratios in terms of maximum stress.
This article examines the combined effects of colony microstructure and stress ratio on long fatigue crack growth in Ti–6Al–4V. The fatigue crack growth rates are compared in lamellar microstructures with fine and coarse lath dimensions produced by controlled cooling (rate) from the β phase field. The effects of β volume fraction are also investigated at stress ratios, R=Kmin/Kmax, between 0.1 and 0.8. The combined effects of the different variables are then modeled using multiparameter concepts. The coarser lamellar microstructures are shown to have better fatigue crack growth resistance than finer lamellar structures. However, β volume fraction is shown to have only a limited effect on fatigue crack growth resistance. Finally, the implications of the results are discussed for microstructural design and fatigue crack growth prediction.
Planar impact experiments are performed on preheated Ti–6Al–4V specimens, at temperatures in the range 25–550 °C, to determine the role of thermal activation on dynamic stress-induced inelasticity and damage. Measurements in this high temperature and high strain rate regime are made possible by modification of the standard plate impact facility to include heating capabilities. This paper describes in detail needed hardware and experimental procedure. A symmetric planar impact configuration is employed to achieve high compressive and tensile stresses in the specimens. The targets are heated by a magnetic field generated by current flow on a coil surrounding the specimen. Interferometric techniques are employed to record the free surface velocity of the target plates. The experimental results show that thermal activation overcomes the role of rate dependence in the material constitutive behavior. The Hugoniot elastic limit (HEL) and spall strength of Ti–6Al–4V significantly decrease with temperature despite the high strain rate, about , used in the tests. The damage mechanism remains the same at high and room temperatures, i.e., microvoid nucleation, growth and coalescence. Microscopy studies, performed on recovered samples, show that temperature substantially reduces the strain inhomogeneity leading to microvoid formation and that a change in void nucleation site occurs. A completely reversible shock-induced phase transformation α→ω appears to be present in the tested Ti–6Al–4V. Evidence of this phase transformation is observed in the velocity histories upon unloading of the first compressive pulse. The phase transformation is controlled by a combination of thermal and stress driven mechanisms.
In this paper, a series of low cycle fatigue tests under multiaxial non-proportional loading at constant room temperature is carried out. It is observed that 63Sn37Pb solder exhibits non-additional cyclic hardening effect under non-proportional loading compared with proportional loading. A damage coupled Ohno–Wang constitutive model is implemented to simulate stress strain loops of solder over a wide range of loading conditions with the consideration of peak stress sharp drop stage. The damage evolution equation proposed by Stolkarts et al. [Stolkarts, V., Keer, L.M., Fine, M.E., 1999. Damage evolution governed by microcrack nucleation with application to the fatigue of 63Sn–37Pb solder. J. Mech. Phys. Solids. 47, 2451–2468.] is modified, in which the sum of maximum shear strain range and normal strain range on the critical plane is adopted as the damage parameter to replace the uniaxial strain range. The reasonable substitution of damage parameter is capable of explaining the difference of damage evolution procedure of tin–lead under proportional and non-proportional loading. Comparison of the experimental results and simulation verifies that the stress strain hysteresis loops and peak stress decline curve of solder can be reasonably modeled with implement of damage coupled constitutive model under proportional and non-proportional loading. The lifetime estimation of 63Sn37Pb based on the assumption of microcrack nucleation governed damage is effective to provide a conservative prediction.
The thermomechanical response of high-strength low-alloy steel (HSLA-65) is discussed. The uniaxial compression tests are performed on cylindrical samples, using an Instron servohydraulic testing machine and UCSD's enhanced Hopkinson technique. True strains exceeding 60% are achieved in the tests, over the range of strain rates from 10 -3/s to about 8500/s and at initial temperatures from 77 to 1000 K. The microstructure of the undeformed and deformed samples is examined through optical microscopy.
The aim of present study is to investigate the electric reaction arising in dry bone subjected to mechanical loadings at high amplitude and low frequency strain. Firstly, specimen is fabricated from femur of cow. Next, the speeds of wave propagation in bone are measured by laser ultra sonic technique and wavelet transform, because these have relationship with bone structure. Secondary, 4-point bending test is conducted up to fracture. Then, electric reaction arising in bone is measured during loading. Finally, cyclic 4-point bending tests are conducted to investigate the electric reaction arising in bone at low frequency strain.
The strain hardening response of INCONEL 690 during tensile deformation between 200–1200°C has been examined. At low temperatures, ⩽600°C, two stages of hardening, associated with dislocation–dislocation and dislocation–solute interactions were observed. Increasing temperatures to 700°C resulted in the introduction of a third hardening stage, transmission electron microscopy suggesting that this additional hardening stage arises because of a transition in the dislocation arrangement from random tangles to a cellular substructure. Finally, from 750°C to 1200°C a single hardening stage was observed, transmission microscopy showing this to be associated with a cellular/sub-grain dislocation substructure. Analysis of these results indicates that the third stage of hardening in INCONEL 690 at temperatures between 600°C and 700°C and single stage hardening between 750°C and 1200°C can be described by the Bodner–Partom (B–P) and/or Kocks–Mecking (K–M) dislocation–dislocation interaction model. Furthermore, between 750°C and 950°C the hardening behavior can be described by the modified K–M dislocation–constant periodic barrier size interaction model. At higher temperatures, >950°C, the modified K–M model may be utilized through inclusion of an experimentally determined strain dependent barrier spacing.
This paper presents an experimental investigation of strain rate effects on polymer-based composite materials. Quasi-static and dynamic experiments at strain rates up to 350 s−1 were performed with end-loaded, rectangular off-axis compression and transverse compression specimens. The dynamic tests were performed on a split-Hopkinson pressure bar, where pulse shaping ensured early dynamic equilibrium and near constant strain rates for all specimen types. The in-plane strain field of the specimen was obtained via digital image correlation. With the high speed camera used for the dynamic tests, the failure process of the specimen was monitored and the fracture angle was measured. The strain rate effect on modulus, yield, ultimate strength, strain to failure and on the in-plane shear properties was studied. The experimental failure envelope for combined transverse compression and in-plane shear loading was compared with the Puck failure criterion for matrix compression and excellent correlation between experimental and predicted failure envelopes was observed for both strain rate regimes. The quasi-static and dynamic yield envelopes for combined loading are also presented.
The thermodynamical description of observed evolution of mechanical properties of shape memory alloys during isothermal simple tension cyclic loading (in pseudoelastic temperature range) is presented. To define the new internal state parameter, the concept of instantaneous residual martensite is introduced. The known form of the free energy function is suitably modified, and the appropriate kinetic equation for the new state variable is proposed. All constants occurring in constitutive equations are determined for special NiTi and CuZnAl alloys. The satisfactory agreement between predicted and experimental stress-strain hysteresis loops is shown.
A constitutive model for large deformation stress–strain behavior and strain-induced crystallization in poly(ethylene terephthalate), at temperatures above the glass transition temperature, is proposed. In this model, the intermolecular resistance is treated in a composite framework where the crystalline and amorphous phases are considered as two separate resistances coupled through two different analog representations leading to the upper and the lower bound approaches. The crystallization rate is expressed following a non-isothermal phenomenological expression based on the modified Avrami equation. Our predicted results are compared to existing experimental results and good agreement is found.
A constitutive model is developed to capture the rate-dependent stress–strain behavior of an amorphous polymer (poly(ethylene terephthalate)-glycol (PETG)) at temperatures in and above the glass transition (θg). As a polymer goes through its glass transition, it exhibits a dramatic decrease in elastic modulus and yield stress, and continues to show strong dependence on strain rate and temperature. The mechanical recognition of the glass transition phenomenon itself depends on the applied deformation rate. The model is able to capture this strong dependence on temperature, strain rate, and strain state for uniaxial and plane strain compression experiments to very large strains. In particular, it captures the dramatic drop in modulus from below to above θg and the corresponding drop in yield or flow stress. The model also captures the dependence on rate, temperature, and state of deformation of strain hardening, including the dramatic stiffening that occurs at very large strains. The model predictions are additionally compared to stress–strain data for poly(ethylene terephthalate) (PET) to identify the areas where strain-induced crystallization plays a role in its compressive mechanical behavior. No significant modifications are needed for the model to capture the behavior of PET in uniaxial compression, in spite of the fact that PET undergoes strain-induced crystallization upon deformation near θg and PETG does not. This suggests that the primary mechanism for dramatic strain hardening in biaxial deformation of PET is not strain-induced crystallization, but rather molecular orientation and alignment.
Stress investigation for the problem of a penny-shaped crack located above the pole of a spherical particle (inhomogeneity) in 3D elastic solid under tension has been carried out. Both the inhomogeneity and the solid are isotropic but have different elastic moduli. The analysis is based on Eshelby's equivalent inclusion method and superposition theory of elasticity. An approximation according to the Saint-Venant principle is made in order to decouple the interaction between the crack and the inhomogeneity. An analytical solution for the stress intensity factors on the boundary of the crack is thus evaluated. It is found that both Mode I and Mode II intensity factors exist, even the loading applied at infinity is uniform tension. Results obtained show that shielding and anti-shielding (amplifying) effects of the inhomogeneity to the crack are solely determined by the modulus ratios of the inhomogeneity to the matrix. Numerical examples also indicate the interaction between the crack and the inhomogeneity is strongly influenced by the distance between the centers.
Retardation of necking under biaxial stretching of bilayer plates comprised of an elastomer layer bonded to a metal layer is studied. Substantial increases in necking limits and consequent energy absorption can be achieved in metal–elastomer bilayers for both quasi-static and dynamic stretching. The phenomena is tied to the fact that under stretching the incremental modulus of the elastomer remains essentially unchanged, or increases, while the incremental modulus of the metal steadily decreases. The effective incremental modulus of the bilayer decreases with stretching but at a lower rate than the metal itself. Since necking instabilities are associated with an erosion of the incremental modulus, necking in the bilayer is delayed to larger strains. Although the strength of a bilayer having the same mass/area as an all-metal plate is reduced, it can nevertheless absorb more energy than the metal plate if the ratio of the elastomer modulus to metal yield stress is sufficiently large. The first part of the paper derives necking limits and energy absorption capacities for bilayers under quasi-static biaxial stretching. The second part of the paper analyses axisymmetric neck development in clamped circular bilayers subject to impulsive pressure loads. The ability of the bilayer to sustain intense impulses is compared to the performance of metal plates of the same material and total mass. Outstanding issues requiring further study are discussed.
Failure in compression of uni-directional fiber composites by fiber kinking is analyzed. General rate constitutive equations for fiber composites are formulated. These equations are used in treating fiber kinking as a problem of localization of deformation. The condition for fiber kinking is compared with previously published results for rigid fibers, and some notable differences are reported. The work unifies theories of kink band and shear band formation.
Top-cited authors
S. Nemat-Nasser
  • University of California, San Diego
Pedro P. Camanho
  • University of Porto
Carlos G. Dávila
A. S. Argon
  • Massachusetts Institute of Technology
Dimitris C. Lagoudas
  • Texas A&M University