Paul Follansbee

• PhD Materials Science and Engineering
• Professor at Saint Vincent College

The interactions of dislocations with idealized obstacle profiles are examined in this chapter. If the obstacle presents a significant enough barrier to continued dislocation motion at a given stress level, the dislocation can pass the obstacle only if the stress is increased or if thermal energy provides the necessary activation. A kinetic model f...

Key findings and conclusions regarding status of the mechanical threshold stress constitutive model are highlighted in this chapter. It is argued that deformation kinetics at constant structure are well described, but that structure evolution, i.e., strain hardening, particularly in context of an isotropic formulation, remains a challenge. Effects...

This chapter builds on the need to separate deformation kinetics at “constant structure” with the kinetics of hardening or structure evolution. Toward this end, the value of defining internal state variables is highlighted. The fundamental equation describing the temperature and dependence of the yield stress is compared with some long-standing cor...

This chapter reviews the early developmental work of the MTS model through application to pure copper, which has often served as a model Face-Centered-Cubic metal. Application to pure nickel is then reviewed. Addition of small additions of carbon to nickel gave a model, solution hardened metal, which required the addition of a second internal state...

Observations and analyses of dynamic strain aging in several metals are revisited. Common experimental trends are reviewed. A model of transport of solutes to a dislocation core is presented and predictions of the model are compared to experimental observations. A key element of the analysis is the influence of strain aging on the rate of structure...

Deformation in the model high entropy alloy CoCrFeMnNi is assessed using an internal state variable constitutive model. A remarkable property of these alloys is the extraordinarily high strain hardening rates they experience in the plastic region of the stress strain curve. Published stress-strain measurements over a range of temperatures are analy...

Deformation in Inconel 718 in the presence of combined effects of the stress anomaly and dynamic strain aging is analyzed according to an internal state variable model formulation. The analysis relies on the availability of experimental data in regimes of behavior where both the stress anomaly and dynamic strain aging are absent. A model that intro...

Strain hardening in austenitic stainless steels is modeled according to an internal state variable constitutive model. Derivation of model constants from published stress-strain curves over a range of test temperatures and strain rates is reviewed. Model constants for this material system published previously are revised to make them more consisten...

Radiation damage in iron-based alloys can lead to an increased strength, accompanied by a decreasing resistance to fracture. While the vast majority of stress-strain curves measured on irradiated material have been at room temperature, quasi-static loading conditions, a few measurements have been performed at other loading temperatures and strain r...

Austenitic stainless steels-particularly the 304 and 316 families of alloys-exhibit similar trends in the dependence of yield stress on temperature. Analysis of temperature and strain-rate dependent yield stress literature data in alloys with varying nitrogen content and grain size has enabled the definition of two internal state variables characte...

The use of a material in a design where failure carries environmental or health and safety risk requires computational design using a conservative strength model. The materials design engineer must determine and be able to justify a lower-bound stress-strain curve. This paper uses the AISI 304 / 304L system to demonstrate how such a model might be...

Published temperature and strain-rate-dependent yield stress data in seven nominally pure bcc metals are analyzed according to a two-obstacle model. A strong intrinsic lattice resistance such as a Peierls barrier and a weaker obstacle representing the collective effects of impurity constituents are combined in a single expression and fit to the ind...

The use of a material in a design where failure carries environmental or health and safety risk requires computational design using a conservative strength model. The materials design engineer must determine and be able to justify a lower-bound stress strain curve. This paper uses the AISI 304 / 304L system to demonstrate how such a model might be...

Long before the complex pressure-temperature phase diagram of plutonium (shown below) was determined, Cyril Stanley Smith’s suggestion that adding small amounts of some impurity atoms to liquid plutonium might retard its undesirable transformation to the brittle alpha phase enabled the fabrication of the world’s first nuclear device tested successf...

A comparison of shear instability in U-Tivs W alloy during high strain rate deformation is presented. Experimental quasi-static and dynamic deformation data are used to formulate the constitutive description based on the mechanical threshold stress model (MTS). The MTS model is used to predict the deformation behavior of U-Ti and W-alloy beyond the...

The materials programs at Los Alamos National Laboratory (LANL) have broadend tremendously since the laboratory was originally founded to support the Mahattan Project, which led to the development of the atomic bomb. Alongside the primary national security mission of the laboratory, collaborations with industry that make use of the special expertis...

A novel experiment has been developed to induce inhomogeneous deformations under simple extension boundary conditions. By appropriate prior cold working of stock material and fabrication of test specimens with tailored dimensions, the location of the deformation zones along the gage length of tensile specimens was controlled. By design, the deforma...

Machining and grinding are well-established material-working operations involving highly non-uniform deformation and failure processes. A typical machining operation is characterized by uncertain boundary conditions (e.g., surface interactions), three-dimensional stress states, large strains, high strain rates, non-uniform temperatures, highly loca...

The stress-strain behavior during the shock rise of a 30 kbar and 54 kbar shock in copper is modeled using a plastic constitutive model that includes rate and temperature dependent hardening and accounts for the transition from thermally activated to viscous drag controlled deformation at high strain rates. A slight modification to the treatment of...

This paper presents an experimental study of the strain-rate and temperature dependence of the yield stress for three low carbon steels (percent c = 0.2, 0.3, and 0.4). Tension test results using notched specimens are reported for temperatures of -20-degrees-C, 0-degrees-C, and 25-degrees-C and strain rates from 10(-4) s-1 to 200 s-1. Two regions w...

Stress-strain measurements and TEM observations in shock-deformed 〈100〉 and 〈111〉 nickel single and polycrystalline samples are reported. When the reload stress measurements of the shock-recovered samples are normalized by the appropriate Taylor factor, the shock-induced strain hardening is found to be similar in all materials studied. Microscopic...

Measurements of yield stress and strain hardening behavior at strain rates in the range 10−3–104s−1 are reported for copper that has been previously shock deformed at a shock pressure of 10 GPa. Characterization of the mechanical properties and microstructure, using transmission electron microscopy, showed that the hardening induced by the shock wa...

Analysis of the strain-rate sensitivity of the yield stress and the strain-rate sensitivity of strain hardening in annealed and quasi-statically and dynamically prestrained Ni270, Ni-510 wt ppm (0.25 at.%) C, and Ni-1900 wt ppm (0.92 at.%) C is presented. Measurements in compression are analyzed according to an internal state variable model where f...

The brittle and/or cleavage fracture behavior of 1008 carbon steel was characterized under dynamic spall loading conditions. The roles of grain size, carbide morphology, and high strain-rate plastic deformation on the spall-induced cleavage fracture were quantitatively estimated following the analysis of Linet al.

The strain-rate and temperature dependent plasticity model of Bammann, as implemented in the PRONTO FEM code, is compared with the model of Kocks and Mecking. It is shown that simplified versions of both models can be directly compared. Both models separate the temperature and strain-rate dependent yield stress (in a well annealed condition) from t...

The deformation behavior of Ti−6Al−4V at temperatures between 76 and 495 K, strain rates between 0.001 and 3000 s−1, and compressive strains to 0.3 has been investigated. Measurements of yield stress as a function of test temperature, strain rate, and prestrain history are analyzed according to the model proposed by Kocks and Mecking. The mechanica...

Shock recovery experiments have been performed to assess the role of residual strain on the substructure evolution and mechanical response of oxygen-free electronic copper. Alterations in momentum trapping design and assembly tolerances produced samples which, while having been all similarly impacted at 518 m s−1 (10 GPa for symmetrical copper impa...

The brittle fracture behavior of 1008 carbon steel was characterized under dynamic spall loading conditions. The role of grain size, carbide morphology, and high strain rate plastic deformation on the spall induced cleavage fracture were quantitatively estimated following the analysis of Lin, Evans, and Ritchie. 7 refs., 2 figs., 14 tabs.

The axisymmetric deformation behavior of 0.9999 Cu is investigated at strain rates from 10-4 to 104 s-1. The variations of the flow stress and of the mechanical threshold stress (the flow stress at 0 K), which is used as an internal state variable, with strain rate and strain are measured. The experimental results are analyzed using a model propose...

A review is given of the development of the Mechanical Threshold Stress (MTS) Model as a description of deformation in metals, particularly at high strain rates. The model is based on the use of internal state variables to represent the current structure or state of the material, and equations are written for the variation of the yield stress with...

Systematic shock recovery experiments have been performed on 6061-T6 Al shocked to pressures of 2, 8, and 13 GPa for 1 second pulse durations. Compression samples EDM machined from the recovered samples show that the mechanical behavior of 6061-T6 saturates rapidly under shock loading. Electron microscope examination reveals a random high dislocati...

Dislocation theory is applied to the superposition of thermal-activation kinetics and phonondrag control. The effect of the various parameters is analyzed in detail; in particular, reasonable dependencies of the mobile dislocation density on stress and structure are accounted for. It is concluded that the transition is generally quite sharp and com...

A program to develop the capability to model metal forming operations is in progress. Two forming operations were chosen as model problems for evaluating the accuracy of existing codes and determining their applicability for these types of problems. Detailed inspection of the parts produced by these operations supplied experimental results for comp...

OFE copper was deformed monotonically to strains in excess of 2.0 by torsion and incrementally in wiredrawing. The monotonic ‘tensile’ curve was established by testing the wiredrawn material, after different increments of strain, in uniaxial tension. We estimate that the strain rate of the wiredrawing process was sec−1. Stress reversal experiments,...

Based upon a study of the independent variation of peak pressure and pulse duration upon the shock loading response of OFE copper, the following conclusions can be drawn: (1) Increasing peak pressure or pulse duration was found to decrease the observed dislocation cell size and increase the yield strength and (2) the influence of pulse duration is...

A numerical investigation of the tensile test using a finite-difference, one-dimensional elasto-viscoplastic code is presented. The influence of strain rate, strain rate sensitivity, and inertia on the development of the axial particle velocity, stress, strain, and strain rate profiles in pure copper is studied. The initial stages of post-uniform d...

A recently developed model for the deformation of copper is reviewed. The model separates the kinetics of structure evolution from those at constant structure and uses the mechanical threshold stress (yield stress at 0/sup 0/K) as an internal-state variable. Predictions of the stress-strain behavior at high strain rates are compared with experiment...

A model for the deformation of copper over a wide range of strain rates has been modified to account for the contribution of dislocation drag at high strain rates. The main effect of adding this mechanism is found in the near yield region at strain rates exceeding 10/sup 3/ s/sup -1/. However, even at strain rates as high as 10/sup 6/ s/sup -1/ the...

Sheet and rod stock of 304L stainless steel were tested in uniaxial tension and compression at strain rates between 10−4 s−1 and 104 s−1. To evaluate the yield locus behavior of the sheet material, multiaxial experiments were performed at a strain rate of 10−3 s−1. We have analyzed these results in terms of existing strain-rate sensitivity, work ha...

The freely expanding ring test (ERT) is a conceptually simple test for determining the stress-strain behavior of materials at large strains and at high strain rates. This test is conducted by placing a thin ring of test material in a state of uniform radial expansion and then measuring its subsequent velocity-time history. The ring is usually prope...

The strain rate sensitivity of a variety of materials is known to increase rapidly at strain rates exceeding ∼10 ³ sec ⁻¹ . This transition has most often in the past been attributed to a transition from thermally activated guide to viscous drag control. An important condition for imposition of dislocation drag effects is that the applied stress, σ...

The height and shape of the obstacle profile for the dominant obstacle provide information on the nature of the deformed microstructure. These quantities can be measured on recovered shock-deformed material. Purpose of this paper is to investigate shock wave deformation mechanisms by measuring the mechanical threshold, or threshold stress, on shock...

In many materials the strain rate sensitivity is known to increase when the strain rate is raised above 1000 s** minus **1. This increase has been interpreted previously as a transition in deformation mechanism from thermal activation control at low strain rate to dislocation drag control at high strain rate. In copper, copper aluminum alloys and s...

The title problem is considered within the theory of incremental elastoplasticity and results of an earlier finite element analysis (Part I) processed to furnish: the indentation response with increasing pressure, contact and interior stresses on loading and unloading, yield region growth, strain distributions, and surface displacement profiles. Th...

The influence of strain rate on the tensile deformation and fracture behavior of powder-fabricated titanium and nickel containing porosity has been investigated. Measurements of uniform strain, local fracture strains, and elongations to failure show that, over the range of strain rates from 10−4 to 102 s−1, there is little or no effect of the strai...

To determine the suitability of the ERT for these fundamental investigations, a series of experiments was performed on a carefully controlled material - oxygen-free electronic fully annealed copper. Recovered ring samples were analyzed and the change in hardness determined. Comparisons of the ERT data with that from Hopkinson bar tests at strain ra...

On présente des mesures du seuil mécanique, ou contrainte seuil, effectuées sur des éprouvettes de cuivre et de Nitronic 40 déformées de manière quasi-statique et dynamique. Les résultats concernant le cuivre montrent que l'accroissement de la contrainte seuil avec la vitesse de déformation est semblable à celui de la contrainte d'écoulement. Dans...

The title problem is treated, under the conditions of frictionless and completely adhesive contact, within the context of incremental elasto-plasticity. The analysis employs a constant-strain-triangle, finite element code, together with a new grid expansion technique which aids computational efficiency. Preliminary results are presented and compare...

A simple cumulative damage model has been developed for the low velocity, normal incidence erosion of ductile metals by spherical particles. The model correlates the computed plastic strain distribution for different impact velocities and materials with the experimentally measured erosion rates. This paper describes the surface and sub-surface chan...

The strain rate sensitivity in a variety of metals is known to increase dramatically when the strain rate exceeds about 10/sup 3/ s/sup -1/. In copper, this behavior is analyzed in terms of the transition in rate controlling deformation mechanism from thermal activation to dislocation drag. Experimental results can be made to agree with a model of...

The split Hopkinson pressure bar or Kolsky which provides a technique for performing compression tests at strain rates approaching 10(4) is discussed. At these strain rates, the small dimensions possible in a compression test specimen give an advantage over a dynamic tensile test by allowing the stress within the specimen to equilibrate within the...

In the high strain rate region of a finite amplitude plastic shock wave constitutive equations need to be strongly history dependent and thus are difficult to use in the description of plastic deformation because the deformation is dominated by a dislocation dynamics which is far removed from quasi-equilibrium conditions. The Johnston-Cilman (1969)...

Elastic wave propagation in the split Hopkinson pressure bar (SHPB) is discussed with an emphasis on the origin and nature of the oscillations that often trail the leading edge of the pressure wave. The authors show that in the conditions of the SHPB test the pressure bars vibrate in the fundamental mode and that elastic wave progapation can be ful...

Moving dislocation experience a damping force because of their interactions with lattice phonons and electrons. Except at velocities close to the transverse sound velocity this force is proportional to the dislocation velocity. A high plastic strain rates dislocations may be required to move so quickly that dislocation damping forces determine the...

This report describes recent progress made in understanding the mechanism of erosion of ductile materials by particles in the 10--100[mu]m diameter range with velocities of 10--50m/s. Additional measurements of erosion rate were made to further elucidate the effects of prior cold work on the erosion of Cu and Cu-6%Al. While prior cold work reduces...

A simple accumulated damage model is proposed for the low velocity erosion of ductile metals by spherical particles. Particular attention is paid to normal incidence. A single normal impact is analyzed using an elastoplastic finite element code, and from this analysis the location and magnitude of the plastic strain reversals occurring under multip...

A simple, accumulated damage model is proposed for the low velocity erosion of ductile metals by spherical particles. Particular attention is paid to the case of normal incidence. A single normal impact is analyzed using an elasto plastic finite element code and from this analysis the location and magnitude of the plastic strain reversals occurring...

The dynamic nature of oxidation and corrosion in industrial hot gas streams is examined in this paper. A formalism to describe the response of an exposed surface to the gas stream dynamics is developed and applied to a dynamic oxidation problem in aircraft gas turbines. Analysis of the conditions in the turbine section of these engines provides an...

Within a prescribed bandwidth, the relative amplitudes of the Fourier components of the gas and surface temperature waves are a simple function of the local heat-transfer coefficient and the thermal properties of the component. This method of measuring the local heat-transfer coefficient is described in this paper and heat transfer coefficients mea...

A new method of constructing thin sensing films directly on superalloy surfaces has been developed and several applications of the technology are described in this paper. In this technique, a component is coated and oxidized to form an adherent, high dielectric strength metal oxide surface layer and arrays of sensing devices are sputtered on the ox...

The use of fine wire thermocouples to measure wide bandwidth combustor and combustor exhaust gas temperatures is described in this paper. The heat transfer to the thermocouples is reviewed and simple expressions for the transfer functions of the thermocouples are developed. Extensive results of measurements in laboratory and gas turbine combustor e...

New surface temperature sensors have been developed for high temperature measurements in gas turbines. A turbine component is coated and oxidized to develop an adherent, high dielectric strength metal oxide on the component surface. Standard platinum and platinum/rhodium alloys are sputtered directly on the oxidized surface to form arrays of thermo...

A new method has been developed for measuring heat transfer coefficients in gas turbine combustor exhaust gases. The special features of the exhaust gas dynamics and the responses of components in the exhaust gases result in simple expressions which relate dynamic exhaust gas and component surface temperature fluctuations to the local heat transfer...

Electric fields have been applied across oxides growing on a high temperature alloy and control of the oxidation of the material has been demonstrated. At present, three-fold increases in the oxidation rate have been measured in accelerating fields and the oxidation process has been completely stopped in a retarding field. The experiments have been...

A steel rail, severely gouged during a rocket-sled test, was the focus of an investigation of the microstructural changes which occur during high-velocity, sliding contact. Metallographic analysis of the damaged rail indicated that the mechanism of gouging probably was a crude machining process in which the sled shoe played the role of a tool. Crac...

Results obtained during the last 10 months cover two areas: modeling of impact event using finite element methods, and experimental measurement of erosion rate of Cu and Cu-Al. (DLC)

The development of a constitutive model based on the use of internal state variables and phenomenological models describing glide kinetics is reviewed. Application of the model to the deformation of fcc metals and alloys is illustrated, with an emphasis on the behavior at high strain rates. Preliminary results in pure iron and 4340 steel are also p...

A simple cumulative damage model has been developed for the low-velocity, normal-incidence, erosion of ductile metals by spherical particles. The model correlates the computed plastic-strain distribution for different impact velocities and materials with the experimentally measured erosion rates. This paper describes the surface and sub-surface cha...

Measurements of the Hugoniot Elastic Limit are compared with measurements of the strain-rate dependent compressive yield stress in several metals. The measurements are analyzed according to standard thermal activation theory. In several cases, only data from material from a single lot are used in the comparison. Results in Ti-6Al-4V, W, Ta, and 101...