Effect Of Stress Triaxiality Research Articles

Block shear strength in thin-walled lean duplex stainless steel fillet welded connection with base metal fracture

This paper investigates the accuracy of different design equations given in design specifications and literatures in determining the block shear strength of the lean duplex stainless steel fillet welded connections with base metal fracture. It points out the problem inherent in the block shear provision specified in the North American cold-formed design specification, which does not consider shear strain hardening. The previous test results have found that full shear strain hardening can be assumed for the carbon steel and ferritic stainless steel welded connections, but not applicable to the thin-walled lean duplex stainless steel welded connections with a higher ratio of the tensile strength to yield stress. Based on the results of finite element analysis including ductile damage simulation, this study reveals that the block shear strength of the lean duplex stainless steel specimens can be determined accurately using the mean between the shear yield stress and the shear ultimate stress. This paper also investigates the effect of stress triaxiality incorporated in the block shear equations found in the literature through comparative analysis with the bolted connection. The effect is shown to be negligible for the thin-walled lean duplex stainless steel welded connection, although higher stress triaxiality is developed in welded connection than in bolted connection. This paper recommends a block shear equation assuming the normal tensile stress in the net area in conjunction with partial shear strain hardening. The recommended equation was found to be more accurate than other equations for determining the block shear strength of the thin-walled lean duplex stainless steel welded connections.

Localization and coalescence of imperfect planar FCC truss lattice metamaterials under multiaxial loadings

This study investigates the effect of stress triaxiality on the failure mechanisms of an-isotropic perfect and imperfect planar FCC (Face Centred Cubic) truss lattice metamaterials. Three types of imperfection have been considered in the numerical modelling, namely, distorted struts, missing struts, and strut diameter variation. In order to maintain constant stress triaxiality during the simulations, a novel numerical framework was developed to overcome computational difficulties within the existing numerical approaches beyond elastic region. Three modes of microscopic localization were observed in perfect and imperfect lattices before failure: crushing band, shear band and void coalescence. A clear separation exists between the three modes of localization depending upon the type and level of defects, as well as the stress triaxiality. Under compressive loading, all lattices fail owing to crushing band; the distorted lattices are prone to shear band localization with increase in distortion, whereas missing lattices majorly fail due to void coalescence at high missing struts defect. Strut diameter variation, within the range of the strut diameters selected, shows no significant influence on the macroscopic mechanical response and strain localization. This work may open the door for predicting failure mechanisms of imperfect lattices under variety of loading conditions.

How stress triaxiality affects cavitation damage in high-density polyethylene: Experiments and constitutive modeling

The aim of this article is to investigate how the stress triaxiality affects the plastic deformation behavior of high-density polyethylene using an approach combining experiments and micromechanics-based modeling. The stress-strain behavior along with the cavitation damage accumulation are experimentally quantified under well-controlled transversal response of hourglass-shaped tensile specimens with different curvature radii in order to set different triaxial stress states in the median cross-section. A constitutive elastic-plastic-damage representation is then presented within a continuum-based micromechanical framework. The model, constrained by the same boundary conditions as the experimental tests, is used to examine the stress triaxiality effects on the separate and synergistic effects of plasticity and cavitation damage micromechanisms that govern the macro-response.

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.

Ductile fracture of high strength steels with morphological anisotropy, Part II: Nonlocal micromechanics-based modeling

The ductile fracture behavior of a high strength steel is addressed in this two-part study using a micromechanics-based approach. The objective of Part II is to propose, identify, and validate a numerical model of ductile fracture based on the Gurson–Tvergaard–Needleman model. This model is enhanced by the Nahshon–Hutchinson shear modification in combination with a generalization of the Thomason coalescence criterion within a fully nonlocal form and relying on a damage-to-crack transition technique. The material model involves parameters of different natures either related to the micro-mechanics of porous materials or to semi-empirical formalisms. The void nucleation model and elastoplastic behavior have been developed and identified in Part I. The other parameters are identified in this part using inverse modeling based on both the numerical results of void cell simulations and the experimental measurements. The model is shown to adequately predict the effect of stress triaxiality and Lode parameter on the fracture strain as well as the fracture anisotropy. While the cup-cone and slant fracture paths in the round bars and in the plane strain specimens, respectively, cannot be captured using the pure continuum approach, the damage-to-crack transition framework reproduces these experimental observations.

On ductile fracture of 30CrMnSiNi2A steel considering effects of stress triaxiality

30CrMnSiNi2A steel is a high-strength low-alloy steel and it is widely used in the defense industry. Its ductile fracture properties were investigated by using a combined experimental-numerical approach to address the need for assessment of structural integrity. The parameters of the Johnson-Cook constitutive model were obtained through quasi-static and dynamic tensile tests on round bar specimens at different temperatures and relevant finite element method iterations. The effects of strain rate and temperature on fracture were studied. The tensile tests on notched round bar specimens were performed to calibrate the fracture strain in the range of high positive stress triaxiality. The tensile tests on butterfly plates and compression tests on short cylindrical specimens covered the fracture properties in the range of low and negative stress triaxiality. The finite element models were computed and the fracture loci in the space of the effective plastic strain to fracture and the stress triaxiality in a wide range from −1/3 to 1.5 were constructed. The parameters of the Johnson-Cook fracture model and Bao-Wierzbicki fracture model were calibrated. It is shown that stress triaxiality has a significant effect on the fracture of 30CrMnSiNi2A steel and the monotonicity of the fracture loci varies in different stress triaxiality range. The Bao-Wierzbicki model is capable of predicting the fracture patterns of the 30CrMnSiNi2A steel in different stress states.

Formability enhancement in hot spinning of titanium alloy thin-walled tube via prediction and control of ductile fracture

The damage and fracture in hot spinning of titanium alloy is a very complex process under the combined effects of microstructure evolution and stress state. In this study, their dependences on processing parameters were investigated by an integrated FE model considering microstructure and damage evolution, and revealing the effects of microstructure and stress states on damage evolution. The results show that the inner surface of workpiece with the largest voids volume fraction is the place with the greatest potential of fracture. This is mainly attributed to the superposition effects of positive stress triaxiality and the smallest dynamic recrystallization (DRX) fraction and β phase fraction at the inner surface. The damage degree is decreased gradually with the increase of initial spinning temperature and roller fillet radius. Meanwhile, it is first decreased and then increased with the increases of spinning pass and roller feed rate, which can be explained based on the variations of β phase fraction, DRX fraction, stress state and tensile plastic strain with processing parameters. In addition, the dominant influencing mechanisms were identified and discussed. Finally, the thickness reduction without defect in the hot spinning of TA15 alloy tube is greatly increased by proposing an optimal processing scheme.

Experimental and Fracture Model Study of Q690D Steel Under Various Stress Conditions

The fracture failure of high-strength steel has an important relationship with the stress state. In order to predict the fracture failure of high-strength steel under different stress conditions, based on the void growth model (VGM), a fracture model which comprehensively considers the effect of stress triaxiality and the Lode parameter on fracture failure is proposed and is called LVGM. A batch of Chinese Q690D high strength steel round rods and plate shaped specimens reflecting different stress states were processed, and the monotonic tensile tests, the scanning electron microscopy tests and the finite element calculation were carried out to study the crack initiation of the specimens. The microscopic mechanism of the fracture damage of the specimens was analyzed. Based on the fracture test results of the specimens and the corresponding finite element analysis, the LVGM parameters of the Q690D high strength steel were calibrated. Finally, the LVGM was used to predict the crack initiation and fracture failure process of the specimens with initial gap. The prediction results are in good agreement with the experimental results, and the LVGM has better prediction accuracy than the VGM.

A study of ultra-low cycle fatigue failure based on a fracture strain energy model

Ductile failure under ultra-low cycle fatigue (ULCF) loading is often the limit service state of a nuclear structure. In the paper, ULCF tests for a C-Mn-Si steel are carried out. It is observed that the fracture displacement decreases as the number of fatigue cycles increases. An energy-based model, which considers the effects of both stress triaxiality and cyclic loading on the critical fracture strain energy, is proposed. Coupled with the new model, finite element analyses of the round notched specimens can predict the equivalent plastic strain and the number of fatigue cycles to fracture within a scatter band of 1.5.

Effect of Stress Triaxiality on Plastic Deformation of Metallic Glasses

Effect of Stress Triaxiality on Plastic Deformation of Metallic Glasses

Behavior of polyethylene under different triaxial stress states: An experimental and numerical study

The behavior of a semi-crystalline polymer under different triaxial stress states is studied through the combination of experimental testing and finite element simulation. Polyethylene round bar specimens with four different notch radii were stretched at crosshead speed of 1 mm/min until fracture. The continuum damage mechanics damage model and Gurson–Tvergaard–Needleman damage model were proposed and applied to the finite element simulation. The results of engineering stress–displacement curves determined from finite element simulation match experimental results. Finite element simulation without considering damage and with the consideration of damage was conducted to determine the damaged and undamaged true stress–strain relationship of polyethylene materials, respectively. Damage evolution model was established based on the degradation of true stress. The finite element model was further applied to study the distribution of stress triaxiality for specimens with different notch radii and the effect of stress triaxiality on damage evolution, critical damage parameters, and fracture strain. The results show that the distribution of the stress triaxiality on the cross section of the specimen is not uniform, and as the stress triaxiality increases, the position where the maximum stress triaxiality occurs moves from the center point to two-third the radius from the center. Furthermore, the damaged true stress and the undamaged true stress increases with the decrease of the stress triaxiality when the strain is below 0.3, but decreases with the increase of stress triaxiality when the strain is larger than 0.3. In addition, it was found that the greater the stress triaxiality, the earlier the onset of damage and the faster the evolution, but the smaller the fracture strain.

A constitutive model coupling damage and material anisotropy for wide stress triaxiality

A constitutive model that can describe the damage evolution of anisotropic metal sheets during the complex forming processes which experience wide stress triaxiality history is essential to accurately predict the deformation and rupture behaviors of the processes. In this study, a modified Lemaitre damage criterion which couples with the anisotropic Barlat 89 yield function is established. The effects of stress triaxiality, Lode parameter and shear stress on damage accumulation are considered in the constitutive model. The model is numerically implemented and applied to fracture prediction in tensile tests with different stress triaxialities and a complex deformation process with wide stress triaxiality history. The good consistency of predictions and experiments indicates that the modified Lemaitre damage model has excellent fracture prediction ability. Finally, the accuracy of the model is analyzed and discussed.

Effects of stress triaxiality and strain rate on the fracture of a CuCrZr alloy

Precipitation hardened Copper-Chromium-Zirconium (CuCrZr) alloy is a prime candidate for divertor components in future European DEMOnstration (DEMO) fusion reactors. To develop the DEMO Design Criteria for In-vessel Components (DDC-IC), the failure criterion of CuCrZr needs to be investigated. Hence, the effects of stress triaxiality and loading strain rate on the fracture of solution heat treated and annealed CuCrZr alloys were studied using digital-imaging-correlation and electron microscopy techniques. It was found that an increase in the stress triaxiality caused a significant decrease of over 50% in the equivalent strain to fracture. On the other hand, increasing applied strain rate from 1.3 × 10−5 s−1to 8.6 × 10−3 s−1 had no considerable effects on the yield stress and elongation. However, higher flow stresses and a larger number density of voids were observed under the highest applied strain rate of 8.6 × 10−3 s−1. Fracture surface analysis showed that the failure model was dominated by void growth and coalescence for all the tests. This work has been performed within the Engineering Data and Design Integration (EDDI) sub-project of the EUROfusion Materials work package and aimed to contribute to the development of the DEMO Design Criteria for In-vessel Components.

The effect of stress triaxiality on the phase transformation in transformation induced plasticity steels: Experimental investigation and modelling the transformation kinetics

In situ multiaxial loading during neutron diffraction tests were undertaken on a low-alloyed Quenched and Partitioning (Q&P) Transformation Induced Plasticity (TRIP) Bainitic Ferrite (TBF) steel with dispersed austenite particles. The effect of stress triaxiality on the evolution of the deformation-induced martensite is investigated under uniaxial- and equibiaxial-tension as well as tension/compression with a ratio of −1:6. It is shown that transformation is not a monotonic function of stress triaxiality; the amount of deformation-induced martensite is similar under uniaxial and equibiaxial tension but it is significantly smaller under tension/compression. The transformation kinetics are modeled using a recently developed kinetic model that accounts for the stress state and the stability and size of the austenite particles. The larger austenite particles transform first and the mean volume of the austenite particles decreases with increasing strain; the decreasing austenite particle size impedes the phase transformation as the deformation proceeds. It is concluded that stress triaxiality alone cannot account for the differences in the transformation kinetics between different loading states and that the number of potential nucleation sites depends on the stress state.

Fracture Prediction for an Advanced High-Strength Steel Sheet Using the Fully Coupled Elastoplastic Damage Model with Stress-State Dependence

In this study, the numerical simulations of sheet metal forming processes are performed based on a fully coupled elastoplastic damage model. The effects of stress triaxiality and Lode angle are introduced into the damage evolution law to capture the loading-path-dependent failure. The proposed constitutive model is implemented into the finite element (FE) code ABAQUS/Explicit via the user-defined subroutine (VUMAT). Next, the identification procedure for DP780 based on the hybrid experimental–numerical method is presented in detail. The numerical results of simple tests are compared with the experiments, and obvious improvement is observed for the proposed model under various loading paths. Finally, the model is applied to predict the edge fracture during sheet blanking process. The predicted global load–displacement responses and crack paths have a good agreement with the experimental results, indicating that the model holds great potentials in simulation of metal forming processes.

Micromechanical modeling of the effect of stress triaxiality on the strain to failure of ductile cast iron

This paper presents modeling of the tensile and failure behavior of different nodular cast iron microstructures under variable stress triaxialities. The model is based on a Representative Volume Element (RVE) approach, which reproduces periodic stochastic distributions of nodules within a 3-D cell. Three cast iron matrices, from fully ferritic to fully pearlitic, are considered as representing the various nodular cast iron classes in relation to strength and ductility. Ductile damage and shear damage models are used for ferrite and pearlite, respectively. Several values of stress triaxiality are applied within the RVE. It is found that numerical results support experimental findings in relation to the local strain distribution and damage initiation and accumulation, reproducing macroscopic tensile responses with good approximation. As highlighted by experiments, triaxiality is found to have a strong effect on material ductility and void volume fraction growth.

A modified Coffin-Manson model for ultra-low cycle fatigue fracture of structural steels considering the effect of stress triaxiality

The ductile crack initiation of structural steels due to ultra-low cycle fatigue (ULCF) loading often governs the limit state in steel structures. This paper proposes a modified Coffin-Manson model for ULCF fracture of structural steels considering the effect of stress triaxiality. To this end, tests on coupon specimens and circular notched specimens made of Chinese Q345qC steel were conducted to form different stress triaxiality states. Based on test results and corresponding finite element analysis, the parameters of modified Coffin-Manson model were determined, and empirical formulas were established between model parameters and stress triaxiality. Finally, detailed finite element analysis was conducted on circular notched specimen tests to validate the proposed model. The results show that the proposed model can be used to predict ULCF fracture of structural steels at different stress triaxialities with high accuracy.

Stress triaxiality effect on cleavage fracture stress

In this work the effect of stress triaxiality on cleavage fracture stress was investigated by means of micromechanical modelling. A unit-cell model was used to determine macroscopic conditions for brittle fracture, in accordance with the slip-induced cleavage fracture model, because of included particle fracture and consequent crack initiation in the matrix. This approach allowed to correlate the critical fracture stress to the particle strength and the ability of the matrix to undergo plastic deformations. Numerical simulations results indicate that the critical fracture stress is strongly dependent on the stress triaxiality, which justify the variability observed in experiments on different specimen geometry. Additionally, the unit-cell modelling allowed to establish a simple relationship between the expected cleavage fracture stress and stress triaxiality, also considering temperature and strain rate. Finally, the use of the plastic constrain factor (defined as the ratio of the critical fracture stress and the yield stress) allows to obtain a master curve that can be used to predict the expected critical fracture stress at different stress triaxiality, temperature and strain rate in different steel grades and alloys.

Effect of stress triaxiality on fracture failure of 6061 aluminium alloy

The effect of stress triaxiality on mechanical properties of 6061 aluminium alloy extruded profiles with different specimens was studied. Macroscopic mechanical property of the various specimen was got through universal testing machine. At the same time, stress triaxiality of different specimens was obtained using the method of finite element simulation. And then the fracture strain of each specimen was outputted by DIC. Fracture modes of 6061 aluminium alloy with different stress triaxiality were studied by SEM. The results show that taking tensile samples as comparison, the cross-sectional area of some notched specimens decreases and the peak load increases. Among them, the minimum cross-sectional area of the R5 central hole specimen is 20% smaller than that of the tensile sample, and the peak load is 28% larger. The fracture strain of the alloy increased with the decrease of stress triaxiality. For the same notch specimens, along the path direction, stress triaxiality of R5 notch specimens, R5 Center-hole specimens and R20 Arc notched specimens increased 47%, 17.8%, 25% respectively. According to the analysis of fracture morphology, the main fracture of 6061 aluminium alloy was ductile fracture. When the stress triaxiality is large, the dimples are small and sparsely distributed, and when the stress triaxiality is small, the dimple is large and evenly distributed. Finally, the Johnson-Cook model material parameters of 6061 aluminum alloy are fitted based on the tensile test results of different shapes of specimens, which can accurately simulate the elastic-plastic deformation and fracture instability of 6061 aluminum alloy under different stress states.

Effects of Size and Distribution of Spheroidized Cementite on Void Initiation in the Punched Surface of Medium-Carbon Steel

In this study, we investigated the effects of the size and distribution of spheroidized cementite on the characteristics of a punched surface as well as the effect of stress triaxiality on the void initiation at the interface between the cementite (θ) and ferrite matrix under shearing deformation. Punching and interrupted punching tests were conducted with two types of annealed medium-carbon steels, θL and θS, which contained large and small cementite particles at low and high densities, respectively. The microstructural deformation in the interrupted punching test was simulated by the finite-element (FE) method. Based on the scanning electron microscopy (SEM) images of the microstructures and microstructural FE models, the stress triaxiality around cementite was identified as an important factor for void initiation. Moreover, the microstructural FE models indicated that a large number of cementite particles reduce the stress triaxiality around them. This mechanism explains why the number of voids in an area away from the surface of θS is smaller than that in an area away from the surface of θL. In contrast, the number of voids near the punched surface was larger in θS than that in θL, owing to the high stress triaxiality caused by the large shearing deformation. The stress triaxiality tended to change the critical equivalent plastic strain for void initiation.