Function Of Plastic Strain Research Articles

Stress Relaxation Cracking in 347H Stainless Steel Arc Welds: Susceptibility Evaluation of Heat-Affected Zone

Stress relaxation cracking (SRC) is considered one of the major failure mechanisms for 347H stainless steel welds at elevated service temperatures or during post weld heat treatment (PWHT), especially within the heat-affected zone (HAZ). This work focuses on the characterization of SRC susceptibility within 347H physically simulated arc welded HAZ at elevated temperatures. A four-step SRC thermomechanical test in combination with finite element modeling (FEM) of the welding and testing processes is developed to establish a susceptibility map for HAZ. The test first runs a thermal cycle with three different peak temperatures (1335, 1275, and 1150 °C) to duplicate representative HAZ subzone microstructures, followed by time-to-failure examination under a variety of pre-stress (260–600 MPa) and pre-strain conditions (0.03–0.19) as a function of reheat temperatures between 750 and 1050 °C. With the aid of FEM, SRC susceptibility maps are generated to identify the threshold stress, plastic strain, and creep strain as a function of test temperature. It was found out that HAZ subzone with a lower peak temperature (1150 °C) appears to be slightly less susceptible to SRC than the other two subzones that experienced higher peak temperatures. Generally, time-to-fracture reduces with increasing initially applied stress and strain for all test temperatures. The pre-stress thresholds decrease from about 500 to 330 MPa as the testing temperature increases from 800 to 1050 °C, while the corresponding initial plastic strain thresholds reduces from 0.15 to 0.06. The SRC susceptibility was also evaluated through the Larson–Miller Parameter (LMP) analysis as a function of plastic strain, initial stress and starting stress upon reaching the testing temperature, respectively. The 1050 °C test with a high pre-applied strain (0.1) exhibits an extremely short time to failure (t = 3 s) that lies outside the general trend in LMP analysis. Additionally, it was identified that a plastic strain above 0.07 is identified to significantly reduce the bulk creep strain tolerance to fracture and therefore increases SRC susceptibility. Hardness measurement and fractography analysis indicated that the strain aging of niobium carbonitrides and other potential phases in conjunction with intergranular precipitates contributes to an increase in microhardness and increased intergranular cracking susceptibility.

Effect of multiaxial strain amplitudes on the cyclic behavior for SN490B steel under proportional loading

SN490B is used in main steel members of high-rise buildings. In this study, multiaxial cyclic tests were conducted on SN490B under a combination of axial tension, compression, and torsion. For a strain amplitude of εa = 0.3%, cyclic softening behavior was observed regardless of multiaxiality. The cyclic softening converged after approximately 100 cycles. However, no significant cyclic softening was observed at εa = 0.5%. The stress variation is expressed as a function of plastic strain. The stress variation equation developed for the cyclic softening and hardening behavior of SN490B accurately approximated the test results.

On the Temperature-Dependence of Deformation-Induced Martensite Formation in AISI 304L Type Steel

In this study, the deformation-induced α-martensite formation in AISI 304L steel was investigated in the temperature range between 75 °C and − 196 °C in the light of the temperature-dependence of hydrogen embrittlement phenomena. For this purpose, tensile tests with in-situ and ex-situ magnetic measurement of the α-martensite volume content as a function of plastic strain were carried out. In addition, a theoretical assessment of the temperature-dependence of the austenite stability was undertaken, evaluating chemical and non-chemical driving force contributions to the martensitic γ → α transformation as proposed by Ghosh and Olson. The experimental results clearly show an increase in the α-martensite volume content and a shifting of the phase transformation to lower strain levels upon reducing the temperature to − 75 °C. A further reduction of the temperature to − 196 °C revealed to have no significant impact on the α-martensite formation. The theoretical assessments indicate a similar temperature-dependence of the austenite stability as observed experimentally and suggest contributions of the thermal friction work at the fcc/bcc interface to be responsible for a constant austenite stability in low-temperature regimes. Additional investigations of deformed microstructures showed that element segregation effects on the local austenite stability are pronounced around room temperature, but become less relevant at low temperatures.

Crack initiation and growth in 316LN stainless steel: Experiments and XFEM simulations

A methodology for computer simulation of ductile fracture in engineering structures using the eXtended Finite Element Method (XFEM) is presented. Crack initiation is modeled using an instability-based failure criterion derived from the micromechanics of void coalescence. The criterion depends on the state of stress at failure, strain hardening and the void volume fraction, whose evolution as a function of plastic strain is obtained using a physics-based void growth law. Material separation is modeled using the cohesive zone method, where cohesive surface elements are dynamically inserted into continuum elements that satisfy the failure criterion. The methodology is illustrated by comparing the model predictions with experimental data on uncracked and pre-cracked 316LN stainless steel specimens. It is shown that, using a set of parameters calibrated from standard tests, the model is able to quantitatively predict fracture in a variety of specimens. In contrast, widely used continuum damage models are unable to predict fracture in the different specimen types using a single set of material parameters.

Energy storage under high-rate compression of single crystal tantalum

When a material is plastically deformed the majority of mechanical work is dissipated as heat, and the fraction of plastic work converted into heat is known as the Taylor-Quinney coefficient (TQC). Large-scale molecular dynamics simulations were performed of high strain rate compression of single-crystal tantalum, and the resulting integral and differential TQC values are reported up to true strains of 1.0. A phenomenological model is proposed for the energy stored in the material as a function of plastic strain with an asymptotic limit for this energy defined by the deformation conditions. The model reasonably describes the convergence of TQC values to 1.0 with increasing plastic strain, but does not directly address the physical nature of thermo-mechanical conversion. This is instead developed in a second more detailed model that accurately accounts for energy storage with two distinct contributions, one being the growing dislocation network and the other the point defect debris left behind by moving dislocations. The contribution of the point defect debris is found to lag behind that of the dislocation network but to be substantial for the high-rate straining conditions considered here.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model verification and validation

The plasticity damage self-consistent (PDSC) model is a damage model developed in the context of continuum damage mechanics in which the damage dissipation potential is formulated to account for damage contributions due to intervoid necking, shearing, and sheeting for an arbitrary stress state. The synergic action of different micromechanisms contributing to ductile fracture is accounted for by their dependence on the plastic deformation, stress triaxiality, third invariant of the deviatoric of the stress tensor, and unilateral conditions. In this work, the PDSC has been implemented in the commercial finite element code MSC MARC via user subroutines and used to predict ductile failure response under different stress state conditions. Firstly, the model implementation has been verified by comparing calculated damage evolution as a function of plastic strain, for prescribed combinations of stress triaxiality and Lode parameter under proportional loading, with an analytical solution. Successively, the model has been validated in predicting ductile fracture for Al6061-T6 in different specimen geometries and comparing with experiment results. Model capability to anticipate fracture initiation conditions, together with specimen global response, and ductile crack propagation also for complex load paths, is demonstrated.

Revealing the Geometrically Necessary Dislocation Density Evolution during Hot Compression of AA7050

Dislocations play a critical role in metal forming processes, and accurate values of dislocation density are important in modelling these processes. However, direct determination of the dislocation density is challenging. In this study, electron backscatter diffraction is used to estimate the evolution of geometrically necessary dislocation density as a function of plastic strain, strain rate and temperature in hot compression of AA7050 alloy. The geometrically necessary dislocation density was found to increase at a higher strain rate and lower temperature; the higher dislocation density in these samples promoted continuous dynamic recrystallisation leading to grain refinement. At lower strain rates and higher temperatures, the dislocation densities were lower and dislocations formed into walls, channels and cells. These observations agree with accepted theories of dislocation evolution and demonstrate the capability of electron backscatter diffraction to provide representative dislocation density values as well as comprehensive information linking plastic flow with microstructural evolution.Keywords: electron backscatter diffraction (EBSD), geometrically necessary dislocations (GNDs), hot deformation, AA7050

A Study on the Effect of Test Temperatures on Tensile and Fracture Behavior of SS 316LN

Abstract In the present study, the influence of test temperatures in the range of 25°C–550°C on the deformation and fracture behavior of SS 316LN has been investigated. The tensile properties and fracture toughness (J1c) of SS 316LN have been evaluated in this temperature range. From tensile properties, strain energy density was estimated as a function of plastic strain and strain-hardening parameters. The fracture tests (J-R curves) are conducted in this temperature range to determine fracture toughness and tearing resistance. From the fracture tested specimens, fractographic studies were carried out to further understand crack initiation mechanisms. From the results of fracture toughness in the temperature range of 350°C–450°C, an attempt to understand the deformation mechanism was made based on an empirical equation.

Analytical prediction of yield stress and strain hardening in a strain gradient plasticity material reinforced by small elastic particles

The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution for strain hardening, i.e. the flow stress as a function of plastic strain, based on a recently developed model for initial yield strength is proposed. The model accounts for random variations in particle size and elastic properties, and is numerically validated against FE solutions in 2D/3D unit cell models. Excellent agreement is found as long as the typical particle radius is much smaller than the material length scale, given that the particle volume fraction is not too large (<10%) and that the particle/matrix elastic mismatch is within a realistic range. Finally, the model is augmented to account for strengthening contribution from shearable particles using classic line tension models and successfully calibrated against experimental tensile data on an Al−2.8wt%Mg−0.16wt%Sc alloy.

Efficient implementation of non-linear flow law using neural network into the Abaqus Explicit FEM code

Machine learning techniques are increasingly used to predict material behavior in scientific applications and offer a significant advantage over conventional numerical methods. In this work, an Artificial Neural Network (ANN) model is used in a finite element formulation to define the flow law of a metallic material as a function of plastic strain ɛp, plastic strain rate ɛ.p and temperature T. First, we present the general structure of the neural network, its operation and focus on the ability of the network to deduce, without prior learning, the derivatives of the flow law with respect to the model inputs. In order to validate the robustness and accuracy of the proposed model, we compare and analyze the performance of several network architectures with respect to the analytical formulation of a Johnson–Cook behavior law for a 42CrMo4 steel. In a second part, after having selected an Artificial Neural Network architecture with 2 hidden layers, we present the implementation of this model in the Abaqus Explicit computational code in the form of a VUHARD subroutine. The predictive capability of the proposed model is then demonstrated during the numerical simulation of two test cases: the necking of a circular bar and a Taylor impact test. The results obtained show a very high capability of the ANN to replace the analytical formulation of a Johnson–Cook behavior law in a finite element code, while remaining competitive in terms of numerical simulation time compared to a classical approach.

On the correlation between plastic strain and misorientation in polycrystalline body-centered-cubic microstructures with an emphasis on the grain size, loading history, and crystallographic orientation

The correlation between plastic strain and crystallographic misorientation, grain size, grain orientation, distance from grain boundary, and loading history were investigated experimentally and numerically for body-centered-cubic (BCC) polycrystalline microstructures based on a misorientation deviation (MD) approach. Nine monotonic tensile experiments were performed on two BCC titanium alloys inside a scanning electron microscope (SEM). The influence of reference orientation was explored both at the grain scale and at the mesoscale using electron backscattered diffraction (EBSD). The correlation between global plastic strain and the MD was quantified. The tendency for orientation change was quantified as a function of plastic strain and grain orientation for three crystallographic orientations (i.e., [100], [110], and [111]) with respect to tensile direction. The subpopulation of small grains exhibited a lower level of misorientation dispersion compared with larger grains, and this discrepancy became more pronounced at higher strains. An empirical equation was proposed to estimate the level of misorientation dispersion for individual grains as a function of grain size and global plastic strain level. Two interrupted in-situ SEM experiments were performed, and this resulted in a significantly increased misorientation compared with uninterrupted tests performed to similar plastic strain levels.

A stress-weighted ductile fracture model for steel subjected to Ultra Low Cycle Fatigue

A new criterion is proposed to simulate the initiation of ductile fracture due to Ultra-Low Cycle Fatigue (ULCF). Building on previous research, the new fracture criterion broadens the scope of ULCF models to account for a broader range of multi-axial stress and strain states that may be encountered in steel structures. The model formulation, supported by observations from finite element plasticity simulations of void growth and fractographic analyses of fracture surfaces, describes damage accumulation as a function of plastic strain, stress triaxiality, and the Lode stress parameter. The damage rate model is integrated over arbitrary cyclic loading histories of local strains and stresses to predict ULCF fracture. The proposed criterion (termed the Stress Weighted Ductile Fracture Model – SWDFM) is supported by a series of 66 coupon scale experiments on two grades of low-carbon structural steel (A572 and A36). These tests interrogate a range of positive and negative stress triaxiality with absolute values between 0.1 and 1.6, Lode stress parameters between 0 and 1, and monotonic and cyclic loading histories. The SWDFM criterion, which requires the calibration of only two material parameters for the materials investigated in this study, is evaluated against the experimental test data using an average-error assessment as well as a cross-validation analysis. Three other ULCF rupture criteria are similarly assessed and compared. The SWDFM is shown to accurately predict ULCF initiation over a wide range of stress states and loading histories, suggesting that the model represents well the micro-mechanical mechanisms of ULCF.

Magnetic, electrical and mechanical properties of Fe40Mn40Co10Cr10 high entropy alloy

A prototypical, single-phase, and non-equiatomic high entropy alloy Fe40Mn40Co10Cr10 has been mechanically deformed at room and cryogenic temperatures. Plastic deformation was accommodated via crystallographic slip at room temperature while transformation induced plasticity (TRIP) has been observed in samples deformed at 77 K. The stress-induced martensitic transformation occurred from face-centered cubic (FCC) to hexagonal close-packed (HCP) structures. A detailed electron backscatter diffraction analysis was utilized to detect phase change and evaluate the evolution of the HCP phase volume fraction as a function of plastic strain. Physical properties of undeformed and deformed samples were measured to elucidate the effect of deformation-induced phase transitions on the magnetic and electrical properties of Fe40Mn40Co10Cr10 alloy. Relatively small magnetic moments along with non-saturating magnetic field dependencies suggest that the ground state in the considered material is ferrimagnetic ordering with coexisting antiferromagnetic phase. The temperature evolution of the coercive fields has been revealed for all samples. The magnitudes of the coercive fields place the considered system into the semi-hard magnetic alloys category. The temperature dependence of the zero-field cooled (ZFC) and field cooled (FC) magnetization was measured for all samples in the low field regime and the origin of irreversibility in ZFC/FC curves was discussed. Besides, the temperature dependence of the resistivity in all samples was measured and the possible conduction mechanisms were discussed.

In-situ X-ray tomography analysis of the evolution of pores during deformation of a Cu-Sn alloy fabricated by selective laser melting

In-situ uniaxial tensile tests coupled with X-ray computed tomography (XCT) were carried out on a Cu-4.3Sn alloy fabricated by selective laser melting. XCT models were constructed to enable step-by-step visualization of pore growth during deformation. Evolution of pores (mean diameter, density, volume fraction and sphericity) was quantified as a function of plastic strain. Evolution of the largest 7 pores existing in the as-printed part are individually characterized and coalescence is graphically presented. Results show that macroscopic instability begins once the largest internal pores reach the surface. Also, accelerated growth and coalescence of the largest 50 pores leads to rapid localization of strain followed by fracture. Pore growth was modeled using the Rice-Tracey (RT) and Huang models for different populations of pores and the parameters were optimized. The RT and Huang constants were found to depend on the initial mean pore diameter.

Development of a mathematical equation describing the strain hardening behaviour of metastable AISI 301 austenitic stainless steel

The strain hardening behaviour of AISI 301 metastable austenite steel was analysed by evaluating tensile data against the empirical mathematical equations of Hollomon, Ludwik and Ludwigson. It was found that these equations were inadequate to model this TRIP steel with low stacking fault energy (SFE). It was found that the fraction of strain-induced martensite could be expressed as a sigmoidal function of the applied strain. The log-log plots of true stress and true plastic strain from 5% to εUTS performed with uniaxial isothermal tests at 30 °C were thereafter adequately fitted with a sigmoidal curve. The instantaneous strain hardening exponent was determined as the slope of the above-mentioned sigmoidal curve at a specific strain value. The strain hardening exponent and the rate of strain hardening dσ/dε) increases with deformation due to formation of strain-induced martensite to a maximum and thereafter decreases as the volume fraction of strain-induced martensite approximates saturation. The variation of the instantaneous strain hardening exponent as a function of plastic strain and the strength coefficient, K, at 30 °C was deduced. A high value of K, 1526MPa, was determined. A correlation between the extent of martensitic transformation and the value of the instantaneous strain hardening exponent was observed. This work is part of the project that seeks to develop a constitutive model describing the flow stress during plastic deformation as a function of both plastic strain and the resulting martensitic transformation at different temperatures and strain rates and which accounts for the isotropic hardening process.

Stress state-dependent mechanics of additively manufactured 304L stainless steel: Part 1 – characterization and modeling of the effect of stress state and texture on microstructural evolution

The effect of stress state and crystallographic texture on strain-induced martensitic transformation kinetics in 304L stainless steel (SS304L) components made by additive manufacturing were investigated. Mechanical tests under uniaxial tension, uniaxial compression, and pure shear were performed. Experimental results showed that the rate of strain-induced martensitic phase transformation, with respect to plastic strain, was highest under uniaxial compression, followed by uniaxial tension, and lowest under pure shear. The higher rate of phase transformation under uniaxial compression than tension in the additively manufactured SS304L contradicts the trends often, but not always, observed in texture-free conventionally processed austenitic stainless steels. The combined effects of stress state, crystallographic texture, and chemistry were studied, for the first time, to develop a new strain-induced martensitic phase transformation kinetics equation for additively manufactured SS304L that captures the microstructural evolution as a function of plastic strain and these factors.

Dislocation-type evolution in quasi-statically compressed polycrystalline nickel

The nature of dislocation generation as a function of applied plastic strain in quasi-statically compressed polycrystalline pure nickel has been studied experimentally at ambient temperature. First, to ensure representative datasets of the geometrically-necessary dislocation densities (ρGND) associated with non-uniform plastic deformation, measurements over large (several millimeter square) areas were made using Hough-based EBSD methods. In addition, the total dislocation density (ρT) responsible for the overall work hardening is estimated from the measured flow stress based on Taylor's hardening model. Next, the statistically stored dislocation (SSD) density (ρSSD) is calculated by subtracting the GND density from the total dislocation density. The results demonstrate that in quasi-statically deformed nickel: i) the measured GND density varies linearly as a function of plastic strain in the range between 0.05 and 0.46; although Ashby's model predicts linearity for GND density evolution over entire range of strains, this study does not cover strains below 0.05; ii) the SSD density increases at a rate much faster than GND density; and iii) the SSD density exceeds the GND density at above 0.09 plastic strain. Both i) and ii) are in agreement with Ashby's prediction, while the magnitudes of GND density (iii) differ from Ashby's model prediction, particularly at large applied strains. Overall, this study enables the interplay of GNDs and SSDs in the hardening of nickel to be gleaned in a quantitative sense. This study illustrates that GNDs are the more important for the strength of polycrystalline metals in the early stages of work hardening, whereas SSDs contribute more to the strength at larger strains. Over the range of strain in this study, work hardening is predominantly through rapid multiplication of SSDs; whereas the GND density is initially higher than SSD density at 0.05 probably due to non-linear evolution of GNDs at low strains (<0.05), which will be the subject of future investigation.

Thermal activation parameters of plastic flow reveal deformation mechanisms in the CrMnFeCoNi high-entropy alloy

To reveal the operating mechanisms of plastic deformation in an FCC high-entropy alloy, the activation volumes in CrMnFeCoNi have been measured as a function of plastic strain and temperature between 77 K and 423 K using repeated load relaxation experiments. At the yield stress, σy, the activation volume varies from ∼60 b3 at 77 K to ∼360 b3 at 293 K and scales inversely with yield stress. With increasing plastic strain, the activation volume decreases and the trends follow the Cottrell-Stokes law, according to which the inverse activation volume should increase linearly with σ−σy (Haasen plot). This is consistent with the notion that hardening due to an increase in the density of forest dislocations is naturally associated with a decrease in the activation volume because the spacing between dislocations decreases. The values and trends in activation volume agree with theoretical predictions that treat the HEA as a high-concentration solid-solution-strengthened alloy. These results demonstrate that this HEA deforms by the mechanisms typical of solute strengthening in FCC alloys, and thus indicate that the high compositional/structural complexity does not introduce any new intrinsic deformation mechanisms.

Simulation of cold work evolution in Ti-1Al-1Mn under deformation and failure

This work proposes thermodynamic model for stored energy evolution in metals within the internal variable approach. It is assumed that stored energy is a function of strain-type variable (structural strain) while dissipated energy is a function of plastic strain. Constitutive equations are derived for one-dimensional case and then generalized to the three-dimensional one. The proposed model is based on the introduction of two independent dissipation potentials with the corresponding multipliers for plastic strain and structural strain. Efficiency of the proposed model is demonstrated by two numerical examples. The first example is a simulation of the energy balance in the process of quasi-static deformation of Ti-1Al-1Mn alloy. The second example is modeling of the fatigue crack growth rate in Ti-1Al-1Mn alloy on the base of the consideration of energy balance at the crack tip. Numerical results have good agreement with the original experimental data.

Issues associated with the use of Yoshida nonlinear isotropic/kinematic hardening material model in Advanced High Strength Steels

The Yoshida nonlinear isotropic/kinematic hardening material model is often selected in forming simulations where an accurate springback prediction is required. Many successful application cases in the industrial scale automotive components using advanced high strength steels (AHSS) have been reported to give better springback predictions. Several issues have been raised recently in the use of the model for higher strength AHSS including the use of two C vs. one C material parameters in the Armstrong and Frederick model (AF model), the original Yoshida model vs. Original Yoshida model with modified hardening law, and constant Young's Modulus vs. decayed Young's Modulus as a function of plastic strain. In this paper, an industrial scale automotive component using 980 MPa strength materials is selected to study the effect of two C and one C material parameters in the AF model on both forming and springback prediction using the Yoshida model with and without the modified hardening law. The effect of decayed Young's Modulus on the springback prediction for AHSS is also evaluated. In addition, the limitations of the material parameters determined from tension and compression tests without multiple cycle tests are also discussed for components undergoing several bending and unbending deformations.