Rate-dependent Plasticity Model Research Articles

A model for the strain rate dependent plasticity of a metastable austenitic stainless steel

A continuum material model is developed for the dynamic plastic deformation behavior of metastable austenitic stainless steel EN 1.4318-2B. An incremental approach in both experimental testing and in the model is used to distinguish between the direct effects of strain rate and the macroscopic adiabatic heating effects. In the model a set of evolution equations is integrated over the deformation path, which makes the model flexible in terms of changes in the strain rate and material temperature. The strain-induced phase transformation from austenite to α′-martensite is accounted for with evolution equations based on the Olson-Cohen transformation model. In order to describe the phase transformation accurately during dynamic loading, the original model is modified by adding instantaneous strain rate sensitivity to the α′-transformation rate. Comparison with experimental results shows that the model can be used to describe the strain rate and temperature dependent behavior of a metastable austenitic alloy with a reasonable number of material parameters. Finally, the model gives realistic results in a set of validation experiments.

Attaining the rate-independent limit of a rate-dependent strain gradient plasticity theory

The existence of characteristic strain rates in rate-dependent material models, corresponding to rate-independent model behavior, is studied within a back stress based rate-dependent higher order strain gradient crystal plasticity model. Such characteristic rates have recently been observed for steady-state processes, and the present study aims to demonstrate that the observations in fact unearth a more widespread phenomenon. In this work, two newly proposed back stress formulations are adopted to account for the strain gradient effects in the single slip simple shear case, and characteristic rates for a selected quantity are identified through numerical analysis. Evidently, the concept of a characteristic rate, within the rate-dependent material models, may help unlock an otherwise inaccessible parameter space.

Quasi-static response and texture evolution of α- and γ-RDX: a comparative study

In this paper, we undertake a comparative study of the stress–strain response and slip activity of α- and γ-polymorph of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) under pressure loading using a rate-dependent single-crystal plasticity model. Texture evolution studies are performed to further understand the effects of the dominant slip systems. The simulations indicate that the difference in elastic moduli and lattice parameters for α- and γ-RDX lead to different elastic–plastic constitutive response in the two polymorphs. γ-RDX exhibits more plastic slip compared to α-RDX for loading on (1 1 1) plane and the two polymorphs have different sets of dominant slip systems. We observe that the high-pressure slip system (0 0 1)[0 1 0] that is determined using molecular dynamics simulations is the most dominant slip system for this orientation. Whereas, for loading on (2 1 0) plane, α-RDX has marginally higher plastic slip than γ-RDX, though the same slip system is dominant for both the polymorphs. The texture evolution for loading on (1 1 1) and (2 1 0) planes follow the path towards the most dominant slip systems for both the polymorphs. We predict that the larger plastic slip in γ-RDX for loading on (1 1 1) plane might play an important role in understanding the reduced sensitivity for shock loading on (1 1 1) plane, when compared to (2 1 0) for which γ-RDX has lesser plastic slip, and (1 0 0) which is purely elastic.

Laser shock processing on Ni-based superalloy K417 and its effect on thermal relaxation of residual stress

The compressive residual stress fields at ambient temperature and stress relaxation at elevated temperatures of nickel-based alloy K417 by laser shock processing (LSP) were investigated by the finite element analysis and experimental method. A temperature and strain rate-dependent plasticity model of Johnson–Cook (JC) material model was utilized to investigate the residual stress evolution under LSP and thermal loads. The residual stress distributions of original and processed specimens were measured by the X-ray diffraction method. Zener–Wert–Avrami function was employed to study the thermal relaxation process of LSP K417, and the simulated results have a significant agreement with the experimental data. Specifically, most of stress relaxation occurs before 30 min of exposure, and the relaxation amplitude increases with the rise of applied temperature. The activation enthalpy of the relaxation process for LSP K417 obtained from simulation and experiment are determined to be 2.86 and 2.85 eV respectively.

Multi-scale structure modeling of damage behaviors of 3D orthogonal woven composite materials subject to quasi-static and high strain rate compressions

We proposed a multi-scale structure modeling scheme to analyze the damage behaviors of three-dimensional orthogonal woven composite materials subject to quasi-static and high strain rate compressions. The multi-scale structure model includes: (1) micro/meso/macro-structure model with periodic boundary conditions for homogenizing the heterogeneous fiber/resin system into unit cells, and (2) a macroscopic rate dependent plasticity model combined with critical damage area failure theory that accounts for the compressive deformation and failure strength of the composite material. The numerical results from the multi-scale structure model provide the locations of stress propagation and the progressive failure behavior within the 3D orthogonal woven composite material. The multi-scale model and the numerical simulation results are validated using compression test results at the strain rate range from 0.001 to 2100 s−1. The methodology we proposed could be applied to understand the microstructure damage mechanisms of 3-D textile composite materials from meso- and macro-structure levels in simpler geometrical model and easier design approaches.

Multi-scale structure finite element analyses of damage behaviors of multi-axial warp-knitted composite materials subjected to quasi-static and high strain rate compressions

This paper reports a multi-scale structure finite element modeling scheme to analyze the damage behaviors of biaxial multi-layer warp-knitted composite materials subjected to quasi-static and high strain rate compressions. The multi-scale structure model includes: (1) a micro/meso/macro structure model with periodic boundary conditions for homogenizing the heterogeneous fiber/resin system into unit cells, and (2) a macroscopic rate-dependent plasticity model for the knitting composite materials combined with critical damage area failure theory, which accounts for the stiffness degradation and failure strength of the material. The finite element results from the model provide the locations of stress propagation, the stress distribution, and the progressive failure behavior within the biaxial multi-layer warp-knitted composite materials. The effects of the knitted yarns and the element number sensitivity of the macro-scale model have also been discussed.

The strengthening effect of carbon nanotube in metal matrix composites considering interphase

The formation of interphase around carbon nanotube (CNT) has been observed experimentally in metal matrix composites (MMCs). However, the characterization of mechanical behavior of interphase and its contribution to the elastoplastic response of MMCs are still open issues. In this paper, a theoretical model is developed to describe the coupled impact of interphase and load transfer effect induced by the reinforcement on the overall mechanical behavior of CNT-reinforced MMCs. The plastic property of interphase is addressed by the rate-dependent amorphous plasticity model. The effective elastic modulus of MMCs is considered to be sensitive to the content of interphase, and the introduction of interphase can obviously enhance the overall strength of the composites. In addition, the effects of matrix grain size, the content and size of the reinforcement have also been addressed in details. The comparisons between the predictions and available experimental data have been performed to validate the applicability of the proposed scheme.

Study on Board-Level Drop Impact Reliability of Sn–Ag–Cu Solder Joint by Considering Strain Rate Dependent Properties of Solder

Board-level drop reliability test and analysis require dynamic characterization of the high strain-rate properties of the solder, along with solder joint failure tests. Relying on just the drop impact analysis of board-level dynamic response (i.e. G-levels and board bending strains) and an oversimplification of deformation response of solder joints (i.e., assuming elastic stress criteria) can lead to misleading conclusions in the physics-of-failure understanding in drop impact tests. In this paper, impact tests were conducted with a split Hopkinson pressure bar test system to study the dynamic response of bulk solder materials. A finite-element analysis of drop impact was conducted by considering different solder constitutive models such as the elastic and strain rate-dependent plastic model to investigate the effect of the solder constitutive model on the dynamic response of the solder joint. The important finding of this study is that the constitutive model used has a major impact on the dynamic response of solder joint stress and strain results. Theoretically, it is predicted that the strain rate-dependent plastic model gave better correlation results than the simple elastic model. A solder joint reliability characterization using the drop impact test with a clamped–clamped boundary condition was investigated for a plastic ball grid array assembly with Sn–Ag–Cu solder and two board surface finishes. In order to assess drop reliability of solder joint with different surface finishes, Charpy test was conducted to evaluate the dynamic strength of the soldered specimen using Sn–Ag–Cu solder and with or without Ni/Au plating.

Application of damage–plasticity models in finite element analysis of punching shear

The paper presents numerical simulations of punching shear in a reinforced concrete slab-column configuration formerly tested in the laboratory. A brief description of the test program at the University of Waterloo is reported. For the simulation, a symmetric quarter of the test configuration is employed. Full three-dimensional finite element discretized geometry is considered together with elastic–plastic reinforcement embedded as truss elements in concrete. Two regularized numerical models of concrete, formulated within elastic–plastic-damage theories, are applied. The first one, called gradient damage, is refined by an additional averaging equation where gradient enhancement involves an internal length scale. In the second one, called rate-dependent damaged plasticity model, a viscoplastic strain rate is introduced. The results for the first model implemented in FEAP and the second model from ABAQUS are discussed in detail. Different issues of numerical simulation to properly predict punching shear behaviour in the slab-column configuration are presented.

Numerical Simulation of Ballistic Impact on Armour Plate with a Simple Plasticity Model

Ballistic impact of a steel projectile on armour steel plate is examined by numerical simulations using 3-D nonlinear dynamic explicit finite element code ANSYS LS-DYNA. Simulations are attempted using a simple strain rate dependent plasticity model that can capture large strain, strain rate hardening and fracture encountered at high velocity ballistic impacts. Initial simulations are carried out for a cylindrical bullet with a semi-spherical nose shape impacting a military vehicle door at two different velocities as a test problem. This is then extended to simulate a real problem of armour piercing shot impact on a thick armour steel plate at ordnance velocity regime. The former is compared with results reported in published literature while the latter is assessed with the experimental findings. The deformation pattern generated in the deformed armour plate, residual projectile velocity and displacement of the projectile are taken as the necessary parameters for evaluating the results of simulation. The study presented in this paper demonstrates the effectiveness of the adopted simple plasticity model to simulate a highly nonlinear phenomenon to reasonably predict the physically measurable impact parameters. Defence Science Journal, Vol. 64, No. 1, January 2014, DOI:10.14429/dsj.64.4521

Identification of the plastic behavior of aluminum plates under free air explosions using inverse methods and full-field measurements

This article describes an inverse method for the identification of the plastic behavior of aluminum plates subjected to sudden blast loads. The method uses full-field optical measurements taken during the first milliseconds of a free air explosion and the finite element method for the numerical prediction of the blast response. The identification is based on a damped least-squares solution according to the Levenberg–Marquardt formulation. Three different rate-dependent plasticity models are examined. First, a combined model based on linear strain hardening and the strain rate term of the Cowper–Symonds model, secondly, the Johnson–Cook model and finally, a combined model based on a bi-exponential relation for the strain hardening term and the strain rate term of the Cowper–Symonds model. A validation of the method and its sensitivity to measurement uncertainties is first provided according to virtual measurements generated with the finite element method. Next, the plastic behavior of aluminum is identified using measurements from real free air explosions obtained from a controlled detonation of C4. The results show that inverse methods can be successfully applied for the identification of the plastic behavior of metals subjected to blast waves. In addition, the material parameters identified with inverse methods enable the numerical prediction of the material’s response with increased accuracy.

Micro-RVE modeling of mechanistic response in porous intermetallics subject to weak and moderate impact loading

In this article we propose macroscopic (continuum) simulation schemes to predict response of porous heterogeneous material systems subjected to weak and moderate impact velocities. The proposed simulation model includes (1) an equation of state for porous solids that describes the evolution of porosity in the material as a function of shock pressure and, (2) a macroscopic rate dependent plasticity model for the porous composite that accounts for the deviatoric strength of the material at weak to moderate shock strengths. In addition, the numerical scheme employs cold-mixture theory to predict shock response of porous intermetallics. The material model is validated using gas-gun impact experiments on Ni/Al Intermolecular Reactive Composite (IRC) at 70% TMD. The proposed model is also used to understand the effect of microstructure on the material response predictions.

On the rheology of dilative granular media: Bridging solid- and fluid-like behavior

A new rate-dependent plasticity model for dilative granular media is presented, aiming to bridge the seemingly disparate solid- and fluid-like behavioral regimes. Up to date, solid-like behavior is typically tackled with rate-independent plasticity models emanating from Mohr–Coulomb and Critical State plasticity theory. On the other hand, the fluid-like behavior of granular media is typically treated using constitutive theories amenable to viscous flow, e.g., Bingham fluid. In our proposed model, the material strength is composed of a dilation part and a rate-dependent residual strength. The dilatancy strength plays a key role during solid-like behavior but vanishes in the fluid-like regime. The residual strength, which in a classical plasticity model is considered constant and rate-independent, is postulated to evolve with strain rate. The main appeal of the model is its simplicity and its ability to reconcile the classic plasticity and rheology camps. The applicability and capability of the model are demonstrated by numerical simulation of granular flow problems, as well as a classical shear banding problem, where the performance of the continuum model is compared to discrete particle simulations and physical experiment. These results shed much-needed light onto the mechanics and physics of granular media at various shear rates.

Rate dependent cyclic behavior simulation of cold worked AISI 316L stainless steel pipe member

This research aims to simulate rate-dependent cyclic behavior of cold worked AISI 316L stainless steel pipe member using a developed FE analysis program. A rate-dependent cyclic plasticity model for cold worked AISI 316L stainless steel is derived based on the monotonic and cyclic loading experiments within quasi-static and dynamic strain rate ranges. Validity of the FE simulation program is presented by comparing analytical results to experimental data. Cyclic behavior of cold worked AISI 316L stainless steel pipe member is clearly simulated as a function of loading rate.

A new strain hardening model for rate-dependent crystal plasticity

This paper presents a crystal plasticity based finite element analysis employing the new microstructure-based strain hardening model recently presented by Saimoto and Van Houtte (2011) [7] to simulate formability and texture evolution in the commercial aluminum alloy 5754. Simulations are performed to compare the predictive capability of the new hardening model against the common work hardening models using a rate-dependent plasticity formulation. The parameters in the numerical models are calibrated using the X-ray data published by Iadicola et al. (2008) [9] for the aluminum sheet alloy 5754. The predictions of the model for balanced biaxial tension and in-plane plane-strain tests are compared against experimental observations presented in Iadicola et al. (2008) [9]. It is concluded that the new model provides the best predictions of the large strain behavior of Aluminum sheet alloy 5754 subjected to various strain paths.

Numerical simulation of piercing using FEA with damage and SPH method

The Smoothed Particle Hydrodynamic (SPH) method as implemented in the commercial code LS-DYNA has been used to solve the problem of piercing a hole in a stamped shock absorber seat. The results are compared to those produced by dynamic analysis using conventional finite element methods with material erosion as implemented in LS-DYNA. The SPH method is suitable for modelling of cracking and tearing phenomena occurring in actual production of the spring seat for some material and process parameters. The SPH stress levels need to be closely interpreted in contour plots than for the FEA results though as high stresses remain in the disconnected volumes. A rate dependent plasticity model is used in the simulation with data produced by mechanical tests of the materials used.

Stability and well-posedness of a rate-dependent strain-softening plasticity model

This paper presents an investigation of the stability and well-posedness of a simple rate-dependent model for strain-softening materials. The model contains key features found in several advanced constitutive models that are currently used for damage and failure of materials. The stability and well-posedness of the model are studied by examining the behaviour of dynamic perturbations to the steady-state solution of a simple shear problem. It is shown that the introduction of strain-rate dependency makes the problem well-posed as dynamic perturbations with all wave lengths remain bounded for finite times. The effect of viscosity on the rate of growth of dynamic perturbations of different wave lengths is shown. It is found that the rate of growth for perturbations with short wave length is severely retarded by the material viscosity.

Characterisation and modelling of short fibre reinforced polymers for numerical simulation of a crash

To save costs, an early validation of functionality is necessary for the crash application of short fibre reinforced polymers by numerical simulation. For this an experimental determination of mechanical values and a numerical material model is essential. In this work the mechanical values of a short fibre reinforced polymer were determined at varied strain rates and in different directions under compression, shear and tension loading. With data of this experiments a new orthotropic-linear elastic and both orthotropic and strain rate dependent plastic material model is developed. It considers the hydrostatic pressure dependency of the hardening material and a failure which is influenced by directions, strain rates und multiaxial states of stresses. The validation of material model and characteristic mechanical values is conducted by simulations of determining experiments of the material behaviour as well as at dynamic impact tests.

Characteristics of the Static and Dynamic Behavior of Steel Piles with a Welded Joint

During welding process to make joints, residual stress is inevitably produced and weld metal should be used. These influence the static and dynamic behavior of steel structures with welded joints, such as steel piles. In steel structures, dynamic mechanical behavior is different to static mechanical behavior. Therefore, to accurately predict the behavior of steel piles with a welded joint under static-dynamic loading, the research on influence of a welded joint on the static and dynamic behavior of steel piles is necessary. For that purpose, a rate-dependent plasticity model was used, considering strain rate hardening and temperature rise. In this paper, the distribution of welding residual stress in a welded joint was computed by using three-dimensional heat conduction analysis and three-dimensional thermal elastic-plastic analysis. The behavior of steel piles with a welded joint under axial static and dynamic loading was investigated by using three-dimensional elastic-plastic finite element analysis, which employed a rate-dependent plasticity model and included residual stress and mechanical properties of weld metal in a welded joint. The rate-dependent plasticity model used in this paper is proposed by the authors based on the static-dynamic loading tests. Numerical analysis results of steel piles with a welded joint were compared to those without a welded joint. In comparison, the characteristics of static and dynamic behavior of steel piles with a welded joint were investigated.

Further investigation of crystal hardening inequalities in (110) channel die compression

A set of geometrically based FCC crystal slip-systems hardening inequalities is analytically investigated in (110) channel die compression for all lateral constraint directions betweenand, following previous analyses of the other two distinct orientation ranges in (110) compression. With all critical slip systems active, it is proved that these inequalities uniquely predict initial lattice stability and finite crystal shearing only in the horizontal channel plane, consistent with experiments for this range of orientations. (The earlier analyses had predicted load-axis stability in both orientation ranges, and lattice stability in one, also commonly found experimentally.) Moreover, it is established that the lateral constraint stress predicted by the hardening inequalities will be less than that given by classic Taylor hardening as this stress evolves with deformation. It is further shown, taking into account experimental stress–strain curves and latent hardening experiments for aluminium and copper, that lattice stability generally can be expected to very large deformations, except perhaps for lateral constraint orientations near theend of the range, which result is consistent with experiment. In appendix A, the possibilities of solutions with a critical slip system inactive are investigated, and predictions of a power law rate-dependent plasticity model are analysed for comparison with the results based on the hardening inequalities.