Plastic Strain Energy Research Articles

A new anisotropic elasto-plastic-damage model for quasi-brittle materials using strain energy equivalence

An anisotropic elasto-plastic-damage model is developed for quasi-brittle materials within the thermodynamics framework. The anisotropic damage is characterized by second-order damage tensors that are different under tensile and compressive loadings. The hypothesis of strain energy equivalence is adopted with two components, including the hypothesis of elastic strain energy equivalence and the hypothesis of plastic strain energy equivalence. The hypothesis of plastic strain energy equivalence is extended from metals to quasi-brittle materials so as to derive the relations of hardening stresses, which are previously assumed between the undamaged and damaged configurations for quasi-brittle materials. A plastic yield criterion is adopted simultaneously with a damage criterion to account for the coupled elasto-plastic-damage behavior under different loadings. The damage criterion can capture larger axial damage in uniaxial tension and smaller axial damage in uniaxial compression as compared with the lateral damage. The Helmholtz free energy functions are derived for three components: elastic, plastic, and damage. The constitutive laws are derived for three scenarios: the elastoplastic behavior without further damage evolution, the damage behavior without further plasticity evolution, and the coupled elasto-plastic-damage behavior. The anisotropic elasto-plastic-damage model is implemented in ABAQUS as a user material (UMAT) subroutine. The coupled constitutive laws in the continuum domain are implemented in an uncoupled way in the discrete domain with three steps, elastic predictor, plastic corrector, and damage corrector. The UMAT is validated in different conditions, including uniaxial, biaxial, and three-point bending tests. The advantage of considering the plastic free energy in anisotropic damage is illustrated through the strength envelope in biaxial loadings. The numerical results generally agree with experimental results, including the stress-strain curves in uniaxial tests, strength envelope in biaxial tests, and load-deflection curves in three-point bending tests.

On the kinetic formulation of fracture fatigue entropy of metals

AbstractThe kinetic concept of the strength of solids is used to determine the fatigue life of stress‐controlled cyclic loading and evaluate the fracture fatigue entropy. Unlike the traditional stress or strain‐based models, this theory uses the applied stress amplitude and the specimen's surface temperature to determine the lifetime. The degradation fraction in each cycle is used to calculate the life cycle. Then the material parameters of the final life equation are obtained for two materials: low carbon steel 1018 and aluminum 7075‐T6. The number of cycles to fracture and the cyclic plastic strain energy ( ) are used to calculate the fracture fatigue entropy (FFE). It is shown that the life cycle prediction of the proposed model agrees well with the experimental results from the literature. Results provide further evidence for the constancy of FFE.

A plastic strain energy method exploration between machined surface integrity evolution and torsion fatigue behaviour of low alloy steel

To explore the evolution mechanism of multistage machining processes and torsional fatigue behaviour based on strain energy for the first time and provide process optimization of axis parts of low alloy steel for service performance, four multistage machining processes were applied to the 45CrNiMoVA steel, including the Rough Turning process (RT), RT+ the Finish Turning process (FRT), FRT+ the Grinding process (GFRT) and RT+ the Finish Turning process on dry cutting condition (FRT0). The result showed that the FRT process’s average low-cycle torsional fatigue life increased by 50% when it evolved from the RT process. The lower surface roughness of Ra 1.3 μm caused the total strain energy to increase by 163.8 Pa mm/mm instead of the unchanged strain energy density, and the crack feature evolved from some specific bulges to flat shear plane characteristics. When the GFRT process evolved from the FRT process, its average fatigue life increased by 1.45 times, compared with the RT process. Plastic strain amplitude decreased by 21%, and the strain energy density decreased by 4% due to more considerable compressive residual stress (−249 MPa). Plastic deformation layer depth had a consistent tendency with surface roughness. In this paper, surface integrity evolutions on cyclic characteristics and fatigue behaviour have also been explained. A fatigue life prediction model based on the energy method for machined surface integrity is proposed.

Strain ratio effects on microstructure discovery and low-cycle fatigue behavior of DP600 steel under cyclic shear path

The fatigue behaviors of dual-phase steels (DP600) under cyclic shear path are studied and the effects of strain ratio are analyzed. Based on twin bridge shear specimens, complete reverse strain-controlled fatigue tests are carried out on DP600 sheet (1.2 mm) under different strain ratios (R = −1, −0.5, 0, and 0.5) with strain amplitudes in the range 0.8–3.0%. DP600 exhibits cyclic softening with a relatively constant softening rate related to amplitude and strain ratio. Smaller loading amplitude and higher strain ratio are beneficial to improve the softening ability of the material. The γ-fiber-type (<111>//ND) texture components are well developed at higher strain ratios, which improve the fluidity of the dual-phase steel, thus making the microstructure deformation more uniform and reducing the risk of damage caused by deformation compatibility. The uniform deformation of the material improves the absorption of plastic strain energy. Therefore, higher strain ratios are beneficial to improve the fatigue life of dual-phase steel.

Low cycle fatigue performance of DP900 steel under cyclic shear paths

AbstractIn this study, a sheet fatigue shear test device is designed and applied to the low‐cycle fatigue testing of DP900 with varying strain amplitudes within the range of 0.5%–6.0%. The microstructure is analyzed by using electron backscatter diffraction, and fracture surfaces are examined via scanning electron microscopy. Results indicate that the material exhibits cyclic softening behavior after the first two cycles of hardening, with a stable softening rate and a high damage evolution rate related to loading amplitude. The variation of the hysteresis curve in the cyclic process is shown. Total plastic strain energy absorbed increases as loading amplitude decreases and it reaches the peak at approximately 1%. The life prediction model based on plastic strain energy density and strain amplitude is verified to be suitable for the cyclic shear path. The influence of microinhomogeneity on the distribution of stress and strain, especially the deformation of martensite, is closely related to the bi‐linear region of fatigue life curve.

Fatigue crack evolution and effect analysis of Ag sintering die-attachment in SiC power devices under power cycling based on phase-field simulation

Sintering Ag materials is a promising candidate for the die-attachments in SiC power devices due to its high melting point and low thermal resistance. However, CTE mismatch between the SiC chips and the substrates causes cracks to develop in the sintered interconnection structures. Power cycling conditions lead to periodic loadings on the Ag sintering die-attachment. The incremental accumulation of plastic strain energy, combined with periodic fluctuations of elastic strain energy, results in the fatigue crack evolutions of the sintered structures. Further, the crack evolutions considerably degrade the thermal and mechanical properties of the interconnect structure, and critically affects the integrity of the heat transfer network and the mechanical structure of the power devices. In this paper, the fatigue crack evolution of Ag sintering die-attachment in the SiC power devices is simulated based on the phase-field models. Moreover, the thermal performance degradations and stress distributions of die-attachment under power cycling are analysed. A methodology based on finite element modelling and phase-field simulation is proposed, realised by Abaqus and its subroutines. The fatigue crack in the Ag sintering die-attachment initiates from the chip-side corner point, then propagates to the chip-side centre point until the formation of a penetrative crack, which achieves a good match with experimental results. Moreover, along with the crack propagation, the thermal distributions in the chip and the stress distributions of the sintering layer are obtained to analyse the degradations of thermal and mechanical performances of Ag sintering die-attachment in SiC power devices.

Time-Dependent Damage Estimation of a High-Rise Steel Building Equipped with Buckling-Restrained Brace under a Series of Earthquakes and Winds

This study investigates the cumulative damage of a 20-story high-rise steel building equipped with buckling-restrained braces (BRB) under the likely occurrence of earthquake and wind events in the design life of the building. The objective of this research is to introduce a method for evaluating the cumulative damage of BRBs under multi-hazard events that are expected to occur during the service life of a high-rise building in order to achieve a safer building. A methodology is proposed using a Poisson point process to estimate the timeline of earthquake and wind events, wherein the events are assumed to be independent in nature. The 20-story high-rise steel building with BRBs is designed according to the Japanese standard and analyzed using the finite element approach, considering nonlinearities in the structural elements and BRBs. The building is analyzed consecutively using the timeline of earthquakes and winds, and the results are compared with those under individual earthquakes and winds. In addition to the responses of the frame such as the floor displacement and acceleration, the damage of BRBs in terms of the damage index, the energy absorption, the plastic strain energy, and the maximum and cumulative ductility factor are evaluated. It is observed that the BRB’s fatigue life under multi-hazard scenarios is a multi-criteria issue that requires more precise investigation. Moreover, the overall building’s performance and BRB’s cumulative damage induced by the sequence of events in the design life of the building is significantly larger than that under an individual event.

Inverse analysis of dynamic failure characteristics of roadway surrounding rock under rock burst

AbstractRock burst is one of the most serious dynamic disasters in the process of coal resources mining, in order to study its occurrence mechanism and the characteristics of its impact on roadways. Based on the No. 25110 working face of Yuejin Mine in Yi Coal Mine and No. 21032 return air uphill event in Qianqiu Mine, combined with geological conditions, shock location, and source waveform, this paper uses numerical simulation to inverse the dynamic response characteristics of roadway surrounding rock under rock burst. The results show that the plastic strain energy density of No. 25110 working face in Yuejin Mine is mainly distributed around the roadway, and the maximum plastic strain energy density is 3.30 × 107 J at 75 ms, all rock masses around the roadway are damaged, and the maximum damage variable value is 0.44. The plastic strain energy density of No. 21032 return air uphill in Qianqiu mine is mainly distributed around the lower side of the roadway, and the maximum plastic strain energy density is 2.68 × 108 J at 80 ms, all rock masses around the roadway are damaged, and the maximum damage variable value is 1.76, indicating that the rock masses at the roof and two sides of the roadway have been damaged after the impact. Based on the results of numerical simulation, the energy gradient criterion of rock burst tendency was proposed, the degree of energy accumulation of surrounding rock is measured by the change amplitude of energy gradient, and the tendency index of rock burst is quantified, which provides a new method for the prediction of rock burst.

Prediction of Cyclic Plastic Strain Energy Density and Fatigue Life of Non-Masing Behavior Materials Without Master Curve

Prediction of Cyclic Plastic Strain Energy Density and Fatigue Life of Non-Masing Behavior Materials Without Master Curve

Low cycle fatigue response of differently aged AA6063 alloy: Statistical analysis and microstructural evolution

Understanding the dynamic structural changes during cyclic deformation of Al-alloys is a discipline of great interest to material technologists. The primary objective of this report is to assess the low cycle fatigue (LCF) behaviour of AA6063 alloy in under-aged (UA), peak-aged (PA) and over-aged (OA) states and to understand the energetic aspects of cyclic plastic behaviour in the background of the nature and density of the dislocations. Two parameters Weibull distribution analyses, for the first time, establish that despite inferior monotonic strength, LCF life of UA alloy is twice compared to PA alloy at higher (≥0.5%) strain amplitudes. This corroborates well with the fact that the cumulative dissipated plastic strain energy density (CPSED) values exhibit reverse variation with applied strain amplitude in the case of UA alloy as compared to PA and OA alloys. TEM analyses confirm that strain-induced vacancy-driven dynamic precipitation causes dramatic cyclic hardening in UA alloy resulting in improved fatigue life. One can also evidence this from the fivefold increase in the plastic strain energy dissipation and 2-times increased of post-fatigue hardness. In contrast, fracture surface analyses and XRD-based dislocation density measurements coupled with TEM examinations reveal that the shearing or by-passing of precipitates by the dislocations in the PA or OA alloys, respectively, lead to strain localization and cyclic softening, and consequently, reduce the plastic strain energy dissipation and lower fatigue life. The study provides important guidelines for the development of high strength Al-alloys with improved fatigue performance.

Fracture Estimation in Ship Collision Analysis—Strain Rate and Thermal Softening Effects

This study examined the effects of the strain rate and thermal softening on large-scale ductile fracture in ship collisions using a rate-dependent combined localized necking and fracture model. A Johnson–Cook type-hardening model, consisting of strain hardening, rate-sensitivity, and thermal softening terms, was adopted together with an associated flow rule. The temperature was treated as an internal state variable and was calculated from the plastic strain energy using a strain-rate-dependent weighting function under fully isothermal and adiabatic conditions. At every time increment, the fracture locus was updated based on the temporal strain rate, whereas the necking locus was coupled with the hardening law, which was dependent on both the strain rate and temperature. The damage indicator framework was used to consider the non-proportional loading paths. The dynamic shell-element failure model was verified through plate-panel penetration tests and applied to a large-scale ship collision analysis involving a struck ship/ship-shaped offshore installation and a supply vessel. The effects of the loading rate and impact energy were assessed in terms of the global behavior of the structure and observed failure modes.

Impact behavior of concrete-filled steel tube with cruciform reinforcing steel under lateral impact load

The objectives of this research are to investigate the behavior of cruciform steel-reinforced concrete-filled steel columns under impact load through experimental and numerical studies. The effects of impact velocity/height, axial pressure, thickness of steel tube and boundary conditions on the impact resistance of composite columns are studied through the tests of 16 specimens. The detailed progressive responses were recorded, including deformation mode, impact force-time history, deflection-time history and axial force-time history. Based on the test results, the impact resistances of steel-reinforced concrete-filled steel tubular columns and concrete-filled square steel tubular (CFST) columns are compared. In addition, FE models of the composite column are established using ABAQUS and validated based on experimental data. The strain rate effect of steel and concrete is considered in the model. The results show that the outer square steel tube effectively protects the internal steel-reinforced concrete. In the impact energy range of 17.02–51.08 kJ, the specimens only suffer minor bending deformation, which shows their excellent impact resistance. The ultimate plastic strain energy of square steel tube (EPT), cruciform steel section (EPS) and concrete (EPC) accounts for 56.4%, 18.2% and 25.4% of the total energy dissipation, which suggests that the steel tube (EPT) is the main energy dissipation mechanism of concrete-filled square steel tube columns.

Prediction and evaluation of fatigue life via modified energy method considering surface processing

To predict fatigue life more accurately, we consider the relationship between static toughness and fatigue toughness in fatigue failure process, the numerical model of total dissipated plastic strain energy (TDPSE) and fatigue life is established. And considering the effect of surface roughness and surface processing coefficient on fatigue life, the life prediction method of TDPSE is modified. In addition, the fatigue life of Non-Masing and Masing materials are predicted by TDPSE and modified TDPSE method, respectively. Compared with TDPSE method, the life estimated by the modified TDPSE method are closer to the test results, and the modified TDPSE method lays a technical foundation for the development of mechanical components.

Experimental study of the hardening process of Ti/Cu bimetal during compression test

The paper presents the results of tensile and compression tests of Ti/Cu bimetal and copper specimens cut out of 12 mm diameter rod. The bimetal was obtained in the extrusion process by permanently connecting a copper core with a circular cross-section with a layer of titanium deposited on its circumference. To initially identify the physical properties, tensile tests on thin-walled bimetallic tubular samples were carried out. The main research was the compression tests of cylindrical samples with variable thickness of the titanium layer and various ratios of the outer diameter to the height of the samples. The main aim of the research was to experimentally evaluate the hardening process of Ti/Cu bimetal during quasi-static compression. The load was applied parallel to the lamination, and the deformation was measured in a direction parallel and perpendicular to the load direction. The study also analysed the process of deformation and destruction at large plastic deformations. The geometrical dimensions of the specimens, i.e. the ratio of the specimen height to the diameter and a slight increase of the thickness of the titanium layer in composite, significantly affects the values of the elastic limit and yield stress, the elastic and plastic strain energy per unit volume, Young’s modulus, as well as the hardening coefficients determined for the compression tests.

Simulated and experimental study on the ultrasonic cutting mechanism of aluminum honeycomb by disc cutter

Aluminum honeycomb, as the core part of sandwich structure, has been widely used in aeronautics and astronautics industry owing to its superior properties. Ultrasonic cutting has a great potential to reduce the machining defects relative to traditional milling. To have an insight comprehension on the ultrasonic cutting mechanism of aluminum honeycomb by disc cutter, a finite element model is developed. It is found that the widened cell wall, which is a typical phenomenon, is generated on the machined surface. A plastic deformation model for cell wall was established based on the plastic strain energy theory to study the relationship between the width of machined cell wall and ultrasonic cutting parameters. Experiments are performed to verify the developed models and study the relationship between cell wall morphologies and cutting parameters. According to that, an alternating up and down cutting process and plastic deformation of material are observed, which is confirmed to be the reason of cell wall widening; a better machining quality of cell wall can be achieved utilizing a greater ultrasonic amplitude and a lower feed speed.

Mechanism and Control of Roadway Floor Rock Burst Induced by High Horizontal Stress

According to the characteristics of rock burst of high horizontal stress roadway floor, the rock burst mechanism of roadway floor was studied with the background of south track roadway Xing’an mine. Based on the deflection theory and energy principle of the slab, the mechanical model of the floor of the roadway under high horizontal stress was established, the stress and energy criteria of rock burst occurred in the floor of the roadway were deduced, the prevention and control measures of the floor pressure relief with large diameter borehole and concrete-filled steel tube pile support were put forward, and the key parameters were determined. By establishing a numerical model, the evolution law of plastic zone, horizontal stress, and elastic strain energy density of roadway floor with or without support is contrastively analyzed. The results show that the effective means to prevent and control the floor rock burst is to cut off the stress transfer path by weakening the hard floor to reduce floor energy accumulation so as to reduce the floor rock burst risk. Based on the above research, field tests were carried out, and the microseismic monitoring results showed that the floor pressure relief of large diameter boreholes and concrete-filled steel tube pile support effectively relieved the floor rock burst and guaranteed the safety and efficiency of roadway excavation. This technology can provide a reference for the prevention and control of floor rock burst of similar roadways.

Effect of nano-clay addition and heat-treatment on tensile and stress-controlled low-cycle fatigue behaviors of aluminum-silicon alloy: Effect of nano-clay addition and heat-treatment

The objective of the present paper is to investigate the stress-controlled low-cycle fatigue behavior of piston aluminum-silicon (AlSi) alloy reinforced with nano-clay particles and T6 heat-treatment. The piston aluminum-silicon alloy strengthened by 1 wt.% nano-clay particles were prepared by the stir casting method and then subjected to the heat-treatment. The optical microscopy analysis demonstrates that heat-treatment changed the size, morphology, and distribution of silicon phases through the microstructure of the aluminum matrix. In addition to tensile tests, stress-controlled low-cycle fatigue experiments at different loading conditions including the variation of the mean stress, the stress rate, and the stress amplitude were conducted at room temperature. The obtained experimental results showed no clear improvement in either mechanical or fatigue properties of the material. Moreover, the density measurements using the Archimedes method reveal a higher content of the porosity in nano-composite. It was observed that the reinforcement (nano-particles and heat-treatment) can change the cyclic behavior of the AlSi alloy, significantly. The cyclic hardening feature of the AlSi alloy changed to cyclic softening and also the fatigue lifetime and the ratcheting resistance decreased after the nano-particles addition and heat-treatment. Through the microstructural analysis, it was indicated that the neglecting of higher kinematics of age hardening in nano-composite was the major source of mechanical properties reduction. In the end, it was shown that the fatigue lifetime of samples can be described adequately utilizing a modified plastic strain energy technique considering the mean stress effect.

Design of an innovative laser-assisted four-point bending forming process for high-stiffened structure of aluminum alloy

High-stiffened structures of aluminum alloy are commonly used on modern aircrafts to meet the requirements of light weight and high stiffness. In this study, the combination of the laser scanning and four-point bending called laser-assisted four-point bending (LAFPB) was proposed to form the high-stiffened structures of aluminum alloy to the product quality. With the analytical model, simulation and experimental bending results, the forming characteristics of LAFPB were investigated. The main results show that the increase of the plastic strain was originated from the elastic strain of the laser scanned area and the “bullying effect” of the adjacent areas which brought about by the mechanical balance reconstruction. In the laser-assisted four-point bending, the initial elastic strain energy inside the part is converted into plastic strain energy under the action of the laser, the plastic strain energy of the workpiece increased by about 250%. It is proved by simulation and experiment that LAFPB can reduce the mechanical force and springback at the same deformation compared with traditional press bending which make a foundation for improving forming quality of high-stiffened structure parts.

A strain energy density based life prediction model for notched components in low cycle fatigue regime

Fatigue life prediction of engineering components is essential for safe operation of mechanical systems. Energy based models have attracted much attention due to the combined considerations of stress and strain behavior, especially in low cycle fatigue regime. In this work, a new plastic strain energy density (PSED) based life prediction model for notched components subjected to cyclic loading is proposed, in which cyclic stress-strain responses under stress- and strain-controlled modes are both introduced. Experimental tests on 304 stainless steel smooth and notched plate/bar components are conducted for calibrations and verifications. The prediction capability of the proposed model is verified by experimental results.

Evaluation of fiber-reinforced and cement-stabilized rammed-earth composite under cyclic loading

In this paper, the cyclic behavior of Rammed Earth (RE) elements is investigated by imposing strain-controlled cyclic loads. RE samples comprise plain soil, Waste Tire Textile Fiber (WTTF)-reinforced specimens (FR), cement-stabilized specimens (CS), and simultaneously reinforced and stabilized (CSFR) specimens. Cyclic properties and responses such as maximum stress, plastic strain, dynamic elastic modulus, damage, and plastic strain energy are evaluated. Two models are also proposed and tested against the experimental data for predicting the plastic strain and damage in different loading cycles. CT-Scan images are also provided for visual inspection of fractures and crack growth. Based on the results, plain and CS samples are found to show the weakest cyclic behavior, since they experience high maximum stress reduction, dynamic elastic modulus deterioration, damage, and plastic strain energy. Extensive and continuous cracks are also detected in these specimens according to CT-Scan images. On the other hand, CSFR specimens enjoy both high strengths induced by cement stabilization and ductility imparted as a result of fiber reinforcement. CSFR specimens with high fiber contents undergo relatively low maximum strength reduction, dynamic elastic modulus deterioration, damage, and plastic strain energy. FR specimens are also found to display relatively decent cyclic behavior. As a result, it is deduced that among the tested soil mixtures, CSFR specimens (with a WTTF content higher than 2%) have the most suitable performance under cyclic loadings.