Influence Of Stress Triaxiality Research Articles

Analysis of time‐dependent mechanical behavior of polyethylene

AbstractNew data analysis based on a spring‐dashpot model is developed to provide very close simulation of stress variation in polyethylene (PE) when subjected to a multi‐relaxation (MR) test. The model consists of a quasi‐static branch and two (long‐ and short‐term) viscous branches. The study shows that viscous stresses applied to the two dashpots and the model parameters can be quantified as functions of displacement (stroke) by simulating closely the stress variation in relaxation. Using these parameters, influences of stress triaxiality and material grade on PE's stress response at relaxation stages are examined, and along with experimental data at the loading stages, spring constants in the two viscous branches are determined. The results indicate that among three PE grades, spring constants and their trend of variation are similar in the long‐term viscous branch, but not in the short‐term counterpart. The results also show that by decreasing specimen gauge length 10 times to increase stress triaxiality, spring constants in the two viscous branches become closer to each other. The work concludes that the new data analysis can determine all parameters in the model, which can then be considered to quantify the role of the viscous stress response for PE's load‐carrying performance.Highlights Use a simple model to simulate complex, multiple relaxation behaviors of PE. Determine all model parameter values to characterize PE's relaxation behavior. Illustrate the effect of stress triaxiality on PE's viscous stress response. Show the similarity and difference of the viscous stress response among 3 PEs.

Continuous damage model for structural steels and weld metals under ultra-low-cyclic loading

For the fracture problem of structural steel under strong earthquakes, a continuous damage model which comprehensively considers the influence of stress triaxiality and Lode parameter was proposed in this paper. According to the variation law of Mises stress under cyclic loading, this model decomposes the effective cumulative plastic strain into isotropic hardening and kinematic hardening components, assuming a linear proportional relationship between the fatigue damage induced by these two components. The basic mechanical properties and constitutive relationships of five common Chinese structural steels and four corresponding weld metals were investigated. The fracture failure tests for both notched round bar specimens and pure shear specimens subjected to monotonic tensile and ultra-low-cyclic loading were thoroughly examined on these materials. The continuous damage model parameters were calibrated by means of test results and complementary finite element simulations. Experimental and numerical simulation results indicate that Q690 high strength steel exhibits cyclic softening behavior, whereas the other steels show cyclic hardening characteristics. For pure shear specimens, plane strain specimens and shear energy dissipation cover plates, the continuous damage model was adopted to simulate and analyze the damage development and fracture failure process of the specimens. The predictions for crack initiation, crack propagation and fatigue life are consistent with experimental results, lending further credibility to the model. The calibrated continuous damage model of various steels provides an effective means for analyzing the ULCF fracture failure of structural steel under intense earthquakes.

Small punch investigation of the dynamic strain aging behaviour and intermediate temperature embrittlement of Inconel 625

In this study, the deformation behaviour and mechanical property evolution of Inconel 625 were studied at different temperatures and deformation rates by using small punch test (SPT). With the increase in the temperature, small punch characteristic parameters decreased, and an approximate platform was found in the temperature range of 300–600 ℃. The dynamic strain aging (DSA) characteristics were observed in the load-displacement curves over a similar temperature range. To analyse the small punch DSA behaviour, the serration types, critical displacement, and maximum load drop were examined. The serration types changed from Type A to Type C when the temperature increased or the deformation rate decreased. The abnormal DSA was proven at around 600 ℃. Then, the influence of the strain rate was analysed and the intermediate temperature embrittlement was found at 600–700 ℃ as the strain rates decreased. Considering the difference between the SPT and the uniaxial tensile test, the influence of stress triaxiality on DSA was discussed. The similar change rule of serration types was presented. SPT was proven to be a reasonable method to evaluate the DSA behaviour which could replace uniaxial tensile test.

Characterization and modeling of damage behavior of a casting aluminum wheel considering inhomogeneity of microstructure and microdefects

For a meaningful description of casting processes on component behavior, the inhomogeneities of the microstructure, microdefects, and mechanical properties including damage behavior in a casting aluminum wheel were experimentally characterized. Both effects of microstructure/microdefects and stress state on damage behavior were determined by performing smooth and notched tensile tests and torsion tests on specimens extracted from different positions. The distribution of microstructure and microdefects in the cast wheel and the corresponding effects on damage development were analyzed using metallography, 3D X-ray CT, and SEM. Casting simulations were performed to determine distributions of local parameters like solidification time, secondary dendrite arm spacing (SDAS), and porosity. It is clear that the ultimate strength and elongation decrease with increasing porosity and SDAS. A material model describing the influence of porosity on flow stress and a damage model describing the relationships of fracture strain with porosity and triaxiality were developed based on the experimental and numerical results. The correlations of yield stress and elongation with porosity were applied to calibrate the models. Additionally, the influence of stress triaxiality on fracture strain was determined using torsion and notched tensile tests for selected porosities and the corresponding inverse simulations. Simulations of the different specimen tests with the developed material model and damage model could satisfactorily describe the experimental results. This method builds a good basis for coupling between casting simulation and structural simulation to optimize manufacturing processes and develop lightweight products. Improving the precision of microdefect calculation in casting simulations and applying of a stochastic model in structural simulations are important future works.

Investigation of extremely low cycle fatigue behavior of low yield strength steel LY225 under different stress states

• Monotonic tensile and ELCF tests were conducted for LY225 low yield point steel. • ELCF fracture behavior between LY225 steel and Q235 steel was compared. • The LCVGM parameters of LY225 steel were calibrated based on the experimental results. • Buckling and ELCF behavior of LY225 steel dog bone specimen were experimental studied. • The LCVGM can well simulate the post buckling ELCF fracture of dog bone specimen. Low yield point steel is frequently utilized in the energy dissipation components of structures because of its good seismic performance. A low yield point steel LY225 subjected to different stress states is experimental investigated in the study by the monotonic tensile tests and extremely low cycle fatigue tests. The test results demonstrate that LY225 steel shows cyclic hardening characteristic as well as dimple fracture failure mode. In addition, LY225 steel exhibits higher deformability and energy dissipation capacity than Q235 low carbon steel, especially in pure shear stress state, the deformation capacity and extremely low cycle fatigue life of LY225 steel are more than twice that of Q235 steel. The Lode parameter enhanced cyclic void growth model (LCVGM) comprehensively considering the influence of stress triaxiality and Lode parameter can be employed to predict the extremely low cycle fatigue fracture. The LCVGM parameters of LY225 steel were determined based on the experimental results. It indicates that the fracture failure of LY225 steel is free from the influence of Lode parameter due to its good shear performance. The monotonic tensile test and extremely low cycle fatigue test were carried out on the LY225 dog bone specimens, and the fracture failure phenomenon after buckling occurred in the test. The post buckling crack initiation and growth process were numerically simulated by the LCVGM of LY225 steel. The prediction accuracy of the LCVGM was verified by comparing the test results and simulations. This study may provide valuable information about the fracture behavior of LY225 steel under various stress conditions, as well as an effective approach to analyze the post buckling fracture process on the member level.

Mechanical Behavior of Alpha Titanium Alloys at High Strain Rates, Elevated Temperature, and under Stress Triaxiality

The paper presents the experimental results of the mechanical behavior of Ti-5Al-2.5Sn alloy at high strain rates and elevated temperature. Flat smooth and notched specimens with notch radii of 10 mm, 5 mm, and 2.5 mm were used. The experimental studies were carried out using the high-velocity servo hydraulic test machine Instron VHS 40/50-20. The samples were heated with flat ceramic infrared emitters on average between 60 s and 160 s. The temperature control in the working part of specimens was carried out in real time using a chromel-alumel thermocouple. The digital image correlation (DIC) method was employed to investigate the evolution of local fields in the gauge section of the specimen. Data on the influence of stress triaxiality on the ductility of Ti-5Al-2.5Sn alloy were obtained under tension with strain rates ranging from 0.1 to 103 s−1 at a temperature of 673 K. It was found that, at 673 K, the ductility of Ti-5Al-2.5Sn alloy increases with the increasing strain rate for both smooth and notched specimens.

The modified GTN-Thomason criterion for modelling of ductile fracture considering shear factor and size effect in micro-scaled plastic deformation

Coarser grains lead to fewer voids on the fracture surfaces of miniaturized workpiece via affecting the void nucleation, while finer grains result in a higher flow strength by influencing void growth. Furthermore, finer grains make the occurrence of normal tensile fracture difficult, but they accelerate the happening of shear-dominated fracture. These insights help the development of ductile fracture criterion by considering the fracture micro-mechanism in micro-scaled plastic deformation. Shear factor and size effect are thus introduced into the newly modified GTN-Thomason criterion to predict the ductile fracture in micro-scaled plastic deformation of copper sheets with different microstructural grain sizes and deformation stress states. The developed criterion is implemented in simulation of deformation process and well validated to be efficient by corroboration of the experimental results and the simulated load-stroke responses and deformation profiles of five sheets with different grain sizes and stress states. According to the accurate simulation results, the influences of stress triaxiality, the normalized third invariant and grain size on void evolution are further analysed. The results show that the increase of the normalized invariant prevents void shear and leads to a better ductility, while the increase of stress triaxiality facilitates the growth of voids to result in a worse ductility. When the deformation with a relatively high normalized invariant has an ignored void shear, the increase of grain size accelerates the onset of void coalescence and the rate of void growth, leading to a rapid failure. However, when the deformation with a relatively low normalized invariant has an unneglected void shear, finer grains increases the rates of void nucleation, growth and shear, causing a smaller fracture strain. These findings and the modified GTN ductile fracture criterion enhance the understanding and prediction of ductile fracture in micro-scaled plastic deformation, respectively, and further facilitate the development of microparts using by deformation-based micro-manufacturing process.

An improved damage-coupled viscoplastic model for predicting ductile fracture in aluminum alloy at high temperatures

Predicting the ductile fracture in aluminum alloys during hot deformation is important for controlling product quality. To this end, this paper proposes an improved damage-coupled viscoplastic model for predicting the ductile fracture in aluminum alloys at high temperatures. For this model, a dislocation-based viscoplastic model is adopted, and a novel high-temperature damage model is further proposed. The proposed damage model considers the temperature and strain rate effects and also the nonlinear characteristics and stress triaxiality effect of damage evolution. The influence of stress triaxiality is evaluated through notched tensile tests conducted at different temperatures. To describe the actual material degradation, the damage variable is coupled with yield criteria according to continuous damage mechanics. Furthermore, the determination of model parameters based on the results of the uniaxial and notched tensile tests at different temperatures is considered in detail. The proposed constitutive model is applied to analyze damage evolution in a hot tensile process and to predict the fracture occurring during an isothermal bulging test, by employing the user-defined material subroutine VUMAT. The experimental and simulation results showed good agreement, thereby proving the validity of the proposed model for predicting the ductile fracture in aluminum alloys during hot deformation. This study introduces a novel damage model for predicting the ductile fracture in materials, such as aluminum alloys and certain metallic materials, dominated by tensile deformation at high temperatures.

Influences of stress triaxiality and local fiber orientation on the failure strain for injection-molded carbon fiber reinforced polyamide-6

In this paper, the influence of the stress triaxiality on the failure strain of short fiber-reinforced composite, manufactured by the injection molding process, is investigated by tensile tests on notched ASTM-D638 specimen and ASTM E1820-01 U-Shape specimens made of a polyamide-6 thermoplastic polymer reinforced with 20% of short carbon fibers (PA6-20CF). From the combined experimental and FEA investigations, a function correlating the failure strain and the stress triaxiality has been developed can be utilized as a failure criterion for complex components made of short fibers reinforced polymers during the design stage, where no direct testing is a viable option.

X-ray computed tomography investigation of dilation of mineral-filled PVC under monotonic loading

The deformation-induced dilation of mineral-filled polyvinyl chloride (PVC) is investigated by means of polychromatic X-ray absorption tomography (XCT). Axisymmetric notched tensile specimens are strained to prescribed elongations using a tensile test apparatus and subsequently scanned by XCT after relaxation. During straining, surface deformations are quantified by digital image correlation (DIC) and contour tracking. The influence of stress triaxiality and strain rate on dilation is investigated by using tensile specimens with three different notch radii, all strained to three deformation levels at two different nominal strain rates. Pronounced reduction of density, corresponding to an increase of volume, is observed for all specimens in the XCT scans, but markedly different relative density distributions are measured for the three geometries. The accuracy of the polychromatic XCT density estimates is evaluated against data obtained with monochromatic synchrotron radiation computed tomography (sr-XCT), and a comparison to surface deformation-based dilation estimates is presented.

A reexamination of high strength steel yield criterion

The high strength steel (HSS) with a nominal yield stress not less than 460 N/mm2 has been increasingly used in engineering structures. An accurate yield criterion which describes the elastoplastic behavior of high strength steels under complex stress states, is significant for the analysis and design of high strength steel structures. For ductile metal materials, the most generally used the von Mises yield criterion neglects the effects of stress triaxiality and Lode angle on the metal plasticity. However, due to the reduce ductility with the increase in strength, such yield criterion may not applicable to HSSs. In the present paper, the tests of six types of specimens are carried out to evaluate effects of stress triaxiality and Lode angle on the plastic behavior of HSSs (Q550, Q690 and Q890). The applicability of von Mises yield criterion is examined firstly using experimental results and finite element analyses. It demonstrates that an appropriate yield function of HSSs should consider effects of the Lode angle while the influence of stress triaxiality is negligible. Based on the experimental and numerical results, a yield function for HSSs is proposed, to essentially simulate the elastoplastic behavior of high strength steel under complex stress states.

Influence of stress triaxiality and strain rate on stress-strain behaviour and dilation of mineral-filled PVC

The influence of stress triaxiality and strain rate on the tensile behaviour of mineral-filled polyvinyl chloride (PVC) is investigated in this paper. Axisymmetric notched tensile specimens with notch radius equal to 20 mm, 5 mm and 2 mm were tested at three nominal strain rates of 0.0001s−1, 0.001s−1 and 0.01s−1. Surface deformations were measured by digital image correlation and contour tracking, employing two orthogonal cameras, whereas infrared thermography was used to measure self-heating. The yield strength of the material was found to be strain rate and pressure dependent. The volume change was estimated from the stretch field in the notch region of the specimens and found to depend on both stress triaxiality and strain rate. A marked increase of temperature was measured at the highest strain rate.

A stress triaxiality-dependent viscoplastic damage model to analyze ductile fracture under axisymmetric tensile loading

The aim of this paper is to gain insight for the transition of fracture initiation sites in notched tensile specimens. For this purpose, a stress triaxiality-dependent viscoplastic damage model was proposed for various types of notched tensile specimens, where the influence of stress triaxiality on damage, damage-free stress-strain curve and viscoplasticity was considered. Also, in this constitutive model, the consistency viscoplastic regularization method was used to solve the pathological mesh-dependent problem due to strain softening. A hybrid experimental-numerical approach was used to calibrate model parameters by using smooth and one type of round-notched tensile specimens. The same set of model parameters was then applied to predict ductile fracture for three other types of round-notched tensile specimens. Good agreement between experimental data and simulation results confirmed the transferability of model parameters to all types of tensile specimens considered and the ability of the proposed constitutive model to predict ductile fracture over a large range of positive stress triaxialities. This study found that at the onset of fracture critical damage parameters for all five types of tensile specimens were relatively constant, and fracture initiation sites in these specimens were associated with critical damage parameters, shifting from the center to the notch root. Therefore, the critical damage parameter was defined as a ductile fracture criterion and the fracture strain for all the five types of tensile specimens was successfully predicted.

A new overall nonlinear damage model for fiber metal laminates based on continuum damage mechanics

Fiber Metal Laminates (FMLs) are hybrid composites made of interlacing layers of thin metal and fiber reinforced layers. In this work, a new overall damage model is developed to estimate the damage of FML considering the influence of stress triaxiality. The parameters of the damage model were determined using tensile test and iterative FE optimization for each sub-layer. Moreover, the stiffness degradation test was carried out to validate the proposed model for FML plain specimen. Additionally, notched FML specimens were used to simulate the material behavior under more complicated states of stress by implementing the proposed damage model in MSC MARC commercial FE code. A reasonable agreement was obtained between the FE and the experimental results for plain and notched FML specimens. The results indicated that the proposed model not only predicts the strong nonlinear behavior of plain and notched specimens, but also can estimate the failure strain with sufficient accuracy.

Influence of stress triaxiality on the failure behavior of Ti-6Al-4V alloy under a broad range of strain rates

The plastic deformation and failure behavior of metals is significantly affected by loading conditions such as stress state, strain rate, temperature and etc. In this study, the tensile behavior of a dual-phase Ti-6Al-4V alloy was investigated and the influences of stress triaxiality, strain rate and temperature were characterized. Specimens with various initial stress triaxialities (0.33, 0.43, 0.52, 0.62, and 0.74 in this work) were designed and tested under quasi-static and dynamic tension. Digital image correlation (DIC) technique was used to accurately determine the local strain on the surface of the specimen during the process of deformation. Combined experimental-numerical method was adopted to acquire the maximum local strain as well as the local stress triaxiality. Results show that the critical point of the specimen always hides in the center of the cylinder and it is unpractical to measure these values directly, therefore calibration is required for both failure strain and stress triaxiality. Moreover, our results indicate that the flow stress of Ti-6Al-4V is significantly affected by the stress condition. The notched specimens display enhanced engineering flow stress (or load capacity) compared with the smooth cylinder. On the contrary, after calibrated by Bridgman’s theory, their true equivalent stresses are actually lower. These findings remind the researchers that special attention should be paid to the effects of stress triaxiality, even the general trend might be wrong.

Development of a damage mechanics based limit strain concept using an enhanced Rousselier model

Several incidents in the past showed the risks of environmental caused accidents, which exceed the design limits of power plant components. According to technical standards, for the evaluation of safety margins usually stress based criteria are used. These criteria are unable to fully utilize the high deformation capabilities of most materials used for power plant components. To overcome this disadvantage, a proposal for a strain based structural integrity assessment (SIA) concept will be made. The proposed SIA concept is based on damage mechanics simulations using an enhanced Rousselier model. Therefore, three extensions were made to the standard Rousselier model. First, the integration of an additional term allowing the prediction of failure under shear stress conditions developed by Nahshon and Hutchinson is presented. Second, the extension with a kinematic term using a back-stress tensor to the Rousselier model to properly describe very low cyclic loading behavior will be described. For the description of the back stress tensor, models developed by Drucker/ Prager, Armstrong/ Frederick and Chaboche are used. Third, the plasticity behavior at low stress triaxialities was improved by replacing the von Mises plasticity law by a Hosford like yield criterion. The extensions were evaluated with a large experimental program using a ferritic and an austenitic steel.For the derivation of the limit strain concept, the different influences of stress triaxiality, component size, non-proportional loading and multiple loading on the limit strains are investigated experimentally and numerically.

Determination of the Values of Critical Ductile Fracture Criteria to Predict Fracture Initiation in Punching Processes

Punching processes are widely used for producing automobile parts, mechanical components, and other parts. To produce highly accurate parts, it is important to estimate the ratio of the sheared surface to the cut surface. Many researchers have applied the finite-element method (FEM) to analyze the ratio of the sheared surface to the fracture surface on cut surfaces by using ductile fracture criteria. However, it is difficult to determine the fracture criteria on the cut surface by tensile tests or bending tests because the punching process involves many complicated steps. In this study, FEM was applied to the punching process to determine the values of critical fracture criteria (C) by using the ductile fracture criteria proposed by Cockcroft and Latham, Oyane, and Ayada. The ductile fracture criteria were compared with the boundary between the shear surface and the fracture surfaces using experiments performed with a simple punching system. The values of the ductile fracture criteria for the fracture initiation of the formed cut surface were predicted under various clearances between the punch and the die with various punch diameters. The influence of stress triaxiality and the effect of punch diameter on the sheared surface length are also discussed.

Extension of the modified Bai‐Wierzbicki model for predicting ductile fracture under complex loading conditions

AbstractThe ductile fracture behaviour of metallic materials is strongly dependent on the material's stress state and loading history. This paper presents a concept of damage initiation and failure indicators and corresponding evolution laws to enhance the modified Bai‐Wierzbicki model for predicting ductile damage under complex loading conditions. The proposed model considers the influence of stress triaxiality and the Lode angle parameter on both damage initiation and the subsequent damage propagation. The model parameters are calibrated for C45E + N steel using a series of mechanical tests and numerical simulations. The enhanced approach is applied to the modelling of various mechanical tests under proportional and non‐proportional loading conditions and successfully predicts the ductile damage behaviour in these tests.

Fracture behaviour at the sharp notch tip of high strength rail steels – Influence of stress triaxiality

This work explores the possibility of using mechanical properties of two types of notch-free specimens to evaluate crack growth resistance of a sharp notch tip. Equivalent plastic fracture strain (εeqf,ηav) of pre-cracked single-edged-notched bending (SENB) specimen is estimated using a model that correlates εeqf,ηav for notch-free specimens with their average stress triaxiality. Finite element modelling is used to establish constitutive equations and variations of stress triaxiality in the two types of notch-free specimens and the pre-cracked SENB specimen. All of the information is then used to predict the critical strain energy density factor (Sc) at a characteristic distance ahead of the sharp notch tip and the corresponding stress intensity factor (KSc) for three high strength rail steels. The predicted KSc values are compared with the experimentally measured mode I critical stress intensity factor (KIc) at temperatures 23, −10, and −40°C. The results show good agreement between KSc and KIc in their variation with temperature, possibly because Sc takes into account both distortional and dilatational strain energy density of the sharp notch tip under small-scale yielding. Results from the study also suggest that a correlation should exist among mechanical properties for notch-free and notched specimens, though their apparent trend of change with temperature may not bear any similarity.

Evaluation of Ductile Damage Parameters under High Stress Triaxiality

The GTN model proposed by Gurson, Tvergaard and Needleman has been widely applied to predict ductile fracture. However, the evaluation of the GTN model under high stress triaxiality has only been reported in a few studies. In this paper, a series of tensile tests on round notched specimens were performed to evaluate the applicability of the GTN model parameters under high stress triaxiality. The evaluation was carried out by comparing the predicted load-displacement curves with experimental results. It was observed the GTN model parameters only depend on the material except the critical void volume fraction. The influence of stress triaxiality on the critical void volume fraction was discussed. A further discussion about the construction of a new void coalescence criterion for the GTN model was also presented in this paper.