Inelastic Deformation Behavior Research Articles

Damage and fracture initiation under shear and compression stress states in the aluminum alloy EN AW6082-T6

The present paper deals with the experimental and numerical analysis of damage and fracture behavior of ductile metals under combined compression and shear loading. Biaxial experiments with the H-specimen using a pneumatic downholder during compression loading and corresponding numerical simulations are discussed. A thermodynamically consistent anisotropic continuum damage model using damage strains is presented. During the experiments strain fields in critical areas of the specimens are monitored by digital image correlation (DIC) technique also showing evolution of deformation in thickness direction of thin sheets. Corresponding numerical simulations reveal the stress states and details of inelastic deformation behavior.

Performance of circular steel tubes infilled with rubberised concrete under cyclic loads

This paper presents a detailed numerical investigation into the inelastic cyclic performance of circular steel tubes filled with rubberised concrete materials. The study considers rubberised concrete infills with relatively high values of up to 60% volumetric rubber replacement of conventional mineral aggregates, which is lacking in existing investigations. Co-existing axial loads of up to 30% of the nominal composite cross-section capacity are also considered. Modified continuum finite element modelling procedures are proposed and employed to account for the high cumulative deformations and damage development of rubberised concrete under cyclic loading. In particular, the influence of crack opening and closure in concrete under cyclic loading is examined and discussed. In addition to full numerical cyclic analyses, idealised monotonic simulations are also proposed and verified to enable computationally efficient representation of the envelope response. Validations of the full-cyclic and envelope-monotonic models are carried out against available experimental cyclic results, indicating the suitability of the models for representing the inelastic response and degradation of confined concrete with high rubber content. Parametric assessments are then undertaken to examine the influence of key material and geometric parameters, including the rubber content, material strength and cross-section properties, on the inelastic large deformation behaviour. The results of the parametric studies are used to quantify the main response parameters, with focus on the member stiffness, moment-axial strength interaction, local buckling criteria and other ductility measures. Based on the findings, modifications are proposed to current design procedures in order to provide a reliable prediction of the inelastic cyclic response characteristics of rubberised concrete filled circular steel tubes. Apart from providing experimentally validated numerical approaches that can be used in future studies, the proposed analytical and design procedures are suitable for implementation in practical assessment and design applications.

Training material models using gradient descent algorithms

High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. We demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.

Modeling of load responses and aging of high strength fibers considering UV-radiation

Long-term illumination can damage the mechanical properties of high strength fiber composites, resulting in the material aging and loss of mechanical properties. To reveal the mechanism of ultraviolet- (UV-) induced damage, in this paper, a nonlinear constitutive model is developed to describe the elastic and inelastic deformation behavior of high strength fibers under UV-radiation and mechanical loadings. Two internal variables are employed to measure the effects of damage caused by UV-radiation and by mechanical loadings, respectively. The Helmholtz free energy function and the evolution equations of these two internal variables are investigated elaborately and given explicitly for high strength fibers. The proposed theoretical model is then applied to analyze the mechanical degradation of high-performance high strength fibers under uniaxial tension. The modulus and strength of the material predicted by the theoretical model match the aging experimental results rather well, which verifies the rationality and accuracy of the present model. This model is expected to predict the evolution of mechanical properties of high-strength fibers under UV-radiation, which can also provide a theoretical basis for the development of anti-UV technology of fiber reinforced composites.

Gradient-enhanced modelling of deformation-induced anisotropic damage in metallic glasses

Recent experimental and computational studies at different scales reveal an apparent flow-induced anisotropy of the inelastic deformation behaviour in metallic glasses (MGs). However, the anisotropic damage behaviour accompanied by the formation of shear bands is not adequately described in the previous constitutive modelling work. In this study, we develop a thermodynamically-consistent, anisotropic damage model incorporating tension–compression asymmetry (TCA) to describe the unique deformation and damage behaviours. The elastic–plastic response, including the normal stress sensitivity and the plastic dilatancy, is captured by the extended Mohr–Coulomb criterion. A second-order damage tensor is adopted for describing the anisotropic damage behaviour of MGs. By augmenting the Helmholtz free energy function to be dependent on the gradient of the free volume concentration and the gradient of the nonlocal damage parameter, the kinetic equations for the corresponding internal variables are derived within the framework of finite deformation continuum thermodynamics. Different material degradations under tension and compression are considered by decomposing the elastic strain tensor into a positive mode and a negative mode in the free energy function, where the tension-strain-induced damage is fully switched on while the compression-strain-induced damage is only partially activated. The influence of the TCA parameter on the damage initiation, crack propagation and shear bands density, as well as the influence of the gradient regularisation parameter on the width of the damage zone, are systematically studied. The proposed damage model is validated by experiments carried on unnotched and notched microcantilever beams. The simulation results show that both the displacement–load curves and the shear band patterns are in good agreement with the experimental observations.

Fatigue life evaluation for notched single-crystal Ni-based superalloys considering inhomogeneous rafting microstructure

Hot-section components made by single crystal (SC) Ni-based superalloys with geometrical discontinuities such as film holes suffer from spatially inhomogeneous rafting of the γ'/γ microstructure due to harsh circumstances. Therefore, low cycle fatigue (LCF) life prediction is critical for ensuring the safety of engineering structures. Within this regard, an energy-based LCF life model is proposed based on the concept of the strain energy gradient by introducing the effect of rafting into the plastic and elastic parts of the strain energy density. The inhomogeneous microstructure degradation of a centre-hole specimen is depicted by stress-assisted rafting and stress-free isotropic coarsening, whereas the inelastic deformation behaviour of materials near the central hole is simulated by a microstructure-sensitive constitutive model. Combined with the concepts of modified strain energy density, effective damage zone and weight function, the proposed life model achieves a good prediction accuracy in ± 2 scatter bands against the experimental data of the centre-hole specimens with different rafting treatments. Finally, the uncertainty of the proposed life prediction model induced by the statistical dispersion of the microstructure is estimated. The results show that the uncertainty of the predicted lifetimes decreases with the rafting extent and fatigue life, even though the distribution of the γ channel width of the alloy with heavily rafting alloys is highly dispersed.

Creep behavior of intermetallic compounds at elevated temperatures and its effect on fatigue life evaluation of Cu pillar bumps

In electronic devices, intermetallic compound (IMC) can normally be found in solder interconnects, and it can pose significant effects on mechanical integrity of interconnects. It is widely accepted that IMC is brittle and normally assumed to be elastic in related mechanical simulations. However, in this work, temperature-dependent inelastic deformation behavior of Cu6Sn5, a common intermetallic compound in lead-free solder joints, was identified to exist at both room temperature and high temperature up to 180 °C and therefore was systematically investigated by nanoindenation. Young's modulus and hardness of IMC generally decreased linearly with increasing temperature. Creep deformation of IMC during dwelling period in nanoindentation was confirmed and further analyzed. The maximum creep displacement was found to increase from 4.90 nm at room temperature to 186.10 nm at 180 °C. Creep stress exponent was found to decrease from 3.32 to 0.37 as temperature rose, indicating significant improvement of deformation capability. Finite element modeling with and without IMC creep shows that inelastic deformation of IMC can compensate the mismatch between adjacent solder and pad in interconnects. Without considering IMC creep, fatigue life of Cu pillar bump can be severely under estimated in modelling.

Numerical analysis of damage and fracture in steel sheets undergoing non-proportional loading paths

The paper deals with the numerical analysis of damage and fracture mechanisms in steel sheets. Newly developed H-specimens are taken from thin sheets and are tested under different biaxial loading conditions. Results of numerical simulations of a series of biaxial experiments are presented showing also the effect of non-proportional loading paths on inelastic deformation behavior and on damage processes. In this context, an anisotropic continuum damage model is presented based on yield and damage conditions as well as evolution laws for plastic and damage strain rates. Different stress-state-dependent branches of the damage criteria are taken into account corresponding to various damage and failure processes on the micro-scale depending on the stress triaxiality and the Lode parameter. Experiments with the biaxially loaded H-specimen have been performed. Results for proportional and corresponding non-proportional loading histories are discussed. During the experiments strain fields in critical regions of the specimens are analyzed by digital image correlation (DIC) technique. Numerical simulations of the experiments have been performed and numerical results are compared with experimental data. Furthermore, based on the numerical analysis evolution of stress variables is examined and stress distributions in critical specimens areas are detected allowing prediction of stress-state-dependent damage and fracture mechanisms. The numerical results also demonstrate the efficiency of the experimental program and the new specimens geometries covering stress states in the shear-tension regime as well as the effect of the loading histories on inelastic deformation and damage behavior in steel sheets.

Inelastic deformation of metallic glasses under dynamic cyclic loading

Dynamic mechanical analysis was performed in two metallic glasses that show markedly distinct β relaxation features. The confined flow defects of free-volume zones and the inelastic deformation behavior result into a significant mechanical hysteresis loop in dynamic cyclic loadings, which is described with a viscoelastic model. Annealing below the glass transition temperature Tg decreases the concentration of free-volume zones. The understanding of the inelastic deformation, which is related to free-volume zones, is critical and may provide a new avenue into the mechanical properties’ improvement of high entropy metallic glasses.

Deformation Behavior and Cavitation of AA2017 at Elevated Temperatures

In this work, deformation behavior of AA2017-T4 at elevated temperatures was studied employing uni-axial tensile and creep experiments. Tensile tests were carried out at temperatures varying 150–500 °C under different strain rates then, a combination of neural network and dynamic material modeling was utilized to construct the processing maps. Furthermore, creep experiments were conducted to assess inelastic deformation behavior of the alloy at temperatures between 150 and 225 °C and stresses in the range of 150 to 230 MPa. Microstructural evaluations were carried out for determination of microstructural changes and formation of voids and cavities within the samples. The results showed that dynamic precipitation could occur during deformation at temperatures 175–225 °C leading to negative strain-rate sensitivity at true strains larger than 0.1. The main softening process was detected as dynamic recovery at temperatures higher than 250 °C however, dynamic recrystallization could also occur at low strain rates and temperatures higher than 400 °C. The activation energies for hot deformation were computed as 380.6 kJ mole−1 at 250–350 °C and it was reduced to 224.7 kJ mole−1 for the range of 350–500 °C. This showed the hard particle could significantly change rate of flow softening. The creep activation energy was determined as 169.5 kJ while the stress-exponent varied between 5.5 and 10.1 at temperatures between 150 and 225 °C indicating that dynamic recovery controlled by dislocation climb could be the governing creep mechanism.

Mechanical strength and physical properties of Oklahoma's igneous basement

From 2009 to 2016, a drastic increase in seismic activity occurred in the Central and Eastern US (CEUS), particularly in the Oklahoma-Kansas region. The majority of hypocenters were focused in the crystalline basement rock. Information regarding the physical properties (elastic wave velocity, peak strength, etc.) of rocks in the CEUS basement to date is sparse. Forecasting future seismic hazard and predicting the in situ response of the crystalline basement requires their geomechanical parameters be adequately constrained. This work assesses the mechanical and petrophysical properties of several sets of basement rocks from Oklahoma to provide a better framework for understanding intraplate seismicity and overall basement deformation in the continental United States. Laboratory experiments were conducted with granite, rhyolite and diabase basement rock samples collected from southern Oklahoma. Evolution of compressional and shear wave velocity with increasing confinement was measured through a series of ultrasonic velocity tests. A suite of uniaxial and triaxial tests were conducted to measure the elastic and inelastic deformation behavior of the basement rocks. Deformation data was evaluated using the Mohr-Coulomb criterion and compared with additional preexisting deformation data of igneous basement rocks. Dynamic and static elastic properties compare favorably with available field measurements and demonstrate the role physical properties can play in varying mechanical behavior. Granitic samples demonstrate moderate variation of intrinsic physical properties can alter elastic properties and failure behavior significantly. Water-weakening in the basement rocks may indicate fluid-assisted processes such as stress corrosion cracking enhance deformation in the crystalline basement.

Experimental and numerical analysis of damage and fracture mechanisms in metal sheets under non-proportional loading paths

New biaxial experiments and corresponding numerical simulations with specimens taken from metal sheets are discussed. Inelastic deformation behavior as well as damage and fracture mechanisms are examined in detail under different biaxial loading conditions with special focus on non-proportional loading paths. In this context, a continuum damage model is presented based on a yield condition and a damage criterion as well as evolution equations for plastic and damage strain rates. The damage criterion takes into account the effect of different processes on the micro-scale depending on the stress state. Experiments with biaxially loaded specimens with newly developed geometries have been performed using proportional and non-proportional loading histories. Strain fields are monitored by digital image correlation technique and fracture surfaces are analyzed with scanning electron microscopy. Numerical simulations of the experiments have been performed and numerical results are compared with available experimental data. In addition, based on the numerical calculations stress distributions in critical specimen’s areas are detected allowing prediction of damage and fracture modes. The results demonstrate the efficiency of the new geometries of the specimens covering a wide range of stress states as well as the effect of the loading paths on damage and fracture behavior in ductile metal sheets.

Dynamic failure and inelastic deformation behavior of SiC ceramic under uniaxial compression

The investigation of the dynamic compressive properties and failure process of ceramics can broaden their applications under extreme conditions. In this study, the online dynamic deformation and failure processof silicon carbide (SiC) ceramic were directly observed in the split-Hopkinson pressure test by high speed photography. The failure strength of the silicon carbide has been quantified as a function of strain rate. There appears to be a critical value (a transition strain rate), above which the strain rate dependency becomes significant. The failure in the dynamic test is an outcome of the concurrent incline major crack and longitudinal micro-cracks. Scanning electronic microscopy (SEM) observation of the dynamic fragments shows that the transgranular fracture dominates the failure process. High-resolution transmission electron microscopy (HRTEM) observation of the post-collected fragments indicates that the local shear stress causes the nucleation of dislocations responsible for the macroscopic inelastic deformation behavior.

Constitutive modeling of plastic deformation behavior of open-cell foam structures using neural networks

This article presents an approach to use neural networks as a constitutive model for the inelastic deformation behavior of open-cell foams or other porous materials. The inelastic deformation behavior of highly porous materials can be very complex and makes the formulation of a closed form constitutive model a very challenging or even impossible task. The presented methods include the creation of a periodic representative volume element (RVE) of the porous structure, the supply of training data by means of finite element simulations using the RVE and the use of trained neural networks within a user material routine (UMAT) for the finite element code ABAQUS. As a proof of concept this approach is applied to relatively simple two dimensional porous structures, where both the homogenized material behavior and a fully resolved porous structure are simulated and compared. The computational effort for simulating a simple foam structure can be reduced by a factor of more than 10,000 using the proposed homogenization approach.

Inelastic Deformation Behaviors of Thermoplastic Resin and Its Short Fiber Reinforced Composite and Prediction

Inelastic Deformation Behaviors of Thermoplastic Resin and Its Short Fiber Reinforced Composite and Prediction

Modeling the rate-dependent inelastic deformation behavior of porous polycrystalline silver films

During the last years more and more investigations on the viscoplastic behavior of sintered silver inter-connections were published. To classify the meaning of the rate-dependency of porous silver films a good model description is necessary. Since different formulations are available and already used, this work focusses on different continuum mechanics modeling strategies for describing the experimental results. Creep tests at different load and temperature levels as well as monotonic hardening tests were conducted. Two different creep approaches and one viscoplastic approach were used to model the rate-dependency. For all approaches, an instantaneous plastic strain was also considered. The models were parameterized by means of inverse modeling and the Finite-Element-Method. Different load scenarios were computed and the solutions compared. It was found that the hardening experiments were correctly predicted by all models. For multiple-hardening-relaxation computations, large differences between the viscoplastic and the creep models were observed. Two possible reasons could be identified and were discussed. Finally, the results obtained were used to give recommendations for different applications in simulation of electronics packaging issues.

A model for coupled inelastic deformation and anisotropic damage behaviour of concrete

AbstractThe present paper describes a simplified model for isotropic damage developed on continuum damage theory. The model characterizes the distinct behaviour of concrete in tension and compression using a unified equivalent strain, which governs the growth of damage. In reality, concrete exhibits distributed micro‐cracking pattern under multi‐directional loads. Therefore, the model is extended to incorporate damage induced anisotropy inherently for a reliable representation of damage, and captures the direction of possible damage evolution. Moreover, the model takes the inelastic behaviour of material into account based on the extended version of Lubliner failure criterion. The model is validated with experimental data. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling of cyclic deformation behaviour of railway disc brakes under thermomechanical loading

AbstractMetallic materials of railway disc brakes exhibit viscoplastic deformation behaviour under cyclic thermomechanical loadings. In this study, a viscoplastic Chaboche model is applied to describe the inelastic deformation behaviour in the braking process incorporating the inhomogeneous variation of temperature. The rate‐dependent hardening behaviour of 28CrMoV5‐8 steel is modelled by employing combined nonlinear isotropic and kinematic hardening rules. Furthermore, a numerical integration algorithms of the constitutive model is developed by using the implicit backward Euler method. The constructed nonlinear algebraic equations are solved by coupling the improved Pegasus method [4] and Newton method. The proposed model is implemented in the finite element code ABAQUS via a user‐defined material subroutine (UMAT). Finally, finite element simulations including sliding friction and heat transfer between disc and pads are performed for the case of an emergency braking. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Molecular Dynamics Simulation of Grain Refinement in a Polycrystalline Material under Severe Compressive Deformation

Grain refinement in a polycrystalline material resulting from severe compressive deformation was simulated using molecular dynamics. A simplified model with four square grains surrounded by periodic boundaries was prepared, and compressive deformation was imposed by shortening the length in the y direction. The model first deformed elastically, and the compressive stress increased monotonically. Inelastic deformation was then initiated, and the stress decreased drastically. At that moment, dislocation or slip was initiated at the grain boundaries or triple junction and then spread within the grains. New grain boundaries were then generated in some of the grains, and sub-grains appeared. Finally, a microstructure with refined grains was obtained. This process was simulated using two types of grain arrangements and three different combinations of crystal orientations. Grain refinement generally proceeded in a similar fashion in each scenario, whereas the detailed inelastic deformation and grain refinement behavior depended on the initial microstructure.

Refinement of Deformation Approach-Based Model of Materials’ Fatigue Damage Kinetics

The experimental data on inelastic cyclic deformation of various metallic materials are analyzed with the aim to determine the mechanisms governing their variation during cyclic loading. Groups of materials with similar kinetics of inelastic deformation are selected, and the analytical relations for their description are proposed. The variation of inelastic strains under conditions of the material fatigue is closely associated with their hardening–softening, which description requires the calculated model of cyclic yield strength variation. The proposed model for the selected groups of materials makes it possible to describe their inelastic deformation and damage behavior under fatigue conditions.