Function Of Stress Triaxiality Research Articles

Stress triaxiality and Lode angle parameters driven phase field coupled finite deformation plasticity formulation of ductile fracture

The effect of stress triaxiality and Lode angle parameters on crack initiation and propagation is investigated using the phase field coupled elasto-plasticity formulation. To accomplish this, a multi-invariants, i.e., first invariant of stress tensor and second and third invariants of deviatoric stress tensor, dependent finite deformation hyperelasto-plasticity is coupled with phase field theory of ductile fracture. The novel ideas include a proposition of a phase field coupled multi-invariants dependent yield function by including the Hosford equivalent stress in the Drucker–Prager yield function in order to accurately predict the ductile response of the material prior to initiation of the failure and the postulation of the threshold energy in the phase field evolution equation defining a measure of the ductility of materials. The measure of ductility is reported in the form of damage initiation surface in terms of threshold plastic energy as a function of stress triaxiality and normalized Lode angle parameters using the Mohr–Coulomb fracture initiation criterion. The model parameters are calibrated based on the available experimental results in the literature considering the stress triaxiality and Lode angle parameters dependent responses of different specimens. The crack initiation and propagation paths predicted by the proposed model under the different states of stress triaxiality and Lode angle parameters, such as axisymmetric tension, plane strain condition, and axisymmetric compression, match with those predicted experimentally in the literature.

Characterization of the asymmetric evolving yield and flow of 6016-T4 aluminum alloy and DP490 steel

6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths, including uniaxial tensile tests with a 15° increment, uniaxial compressive and simple shear tests with a 45° increment, and biaxial tensile tests using cruciform specimens. Cruciform specimens in the rolling/transverse and 45°/135° sampling directions were tested with seven and four different stress ratios, respectively. The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield. Meanwhile, the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow. Several existing asymmetric yield criteria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel. The results suggest that in the investigated yield criteria, the non-associated models can predict the tension and compression asymmetry of materials more accurately than the associated models, and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant. In addition, the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions, and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours. The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane directions of plastic strain rate, but also further check the diagonal plane directions of plastic strain rate. Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.

A comparative study of three forms of an uncoupled damage model as fracture judgment for thin-walled metal sheets

Ductile fracture always occurs in plastic forming processes of thin-walled metal sheets. Damage models, both coupled and uncoupled ones, have been extensively developed to predict fracture of the sheets. Among these, uncoupled damage models, owing to their simple form are widely used. While for an uncoupled damage model, there exist three forms for its fracture prediction: (1) damage threshold (DT), which is related to the damage accumulation; (2) fracture strain (FS), which is always a function of stress triaxiality and Lode parameter; (3) fracture forming limit diagram (FFLD), which is always related to the principal strains. However, for an uncoupled damage model, its three forms (DT, FS and FFLD) for fracture prediction have never been compared before, and thus scholars have always been confused about how to choose the right form of the three in different loading processes. To clarify this confusion, two popular uncoupled damage models of the MMC4 and DF2016 are embedded into an anisotropic yield function first. Then the above-mentioned three forms of the two models are separately applied for fracture prediction in shear test, dog-bone specimen tensile test, hole specimen tensile test, notched specimen tensile test, bulging test in proportional loadings, and a complex non-proportional loading process of spin forming, respectively. Finally, the predicted results with these three forms are systematically compared and a new explanation for their applicability under different stress states is displayed.

Structural Integrity Assessment of Defected Gas Pipelines Using a Simplified Ductile Damage Model

Abstract The finite element method using the damage model has been increasingly used to predict the failure of various structures. Thus, various damage models were presented, and recently, a phenomenological model called the local fracture strain model was presented, making it easy and accurate to predict the damage of the structure. This model has the advantage of defining fracture strain as a function of stress triaxiality with only a few notched tensile tests but has a limitation because it does not consider the damage evolution because of the void growth. This study presents an enhanced damage model that improves the accuracy of the failure simulation of defected structures by adding a parameter that considers stiffness degradation according to void growth to the damage model based on the fracture strain. Therefore, loading–unloading tests were conducted and the damage index of fracture was identified using a three-dimensional digital image correlation system. The failure simulation results using the proposed damage model were compared with experimental, such as notched tensile, single edge notched tension (SENT), and full-scale burst tests.

Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams

This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and $$300\,\hbox {kg/m}^{3})$$ . Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for each setup using finite element analysis, as the tests were replicated with numerical models. The displacement at failure recorded in the experiments was imposed for the models, determining the failure strain as a function of stress triaxiality and the Lode angle parameter. The results were validated through the analysis of the failure of sandwich structures with aluminium faces and PUR cores.

Experimental stress state-dependent void nucleation behavior for advanced high strength steels

The influence of microstructure and stress state, as defined by the stress triaxiality and Lode parameter, on micro-void nucleation was evaluated experimentally for two 800 MPa Advanced High Strength Steels (AHSS), one a Complex-Phase CP800 alloy, with a ferritic-bainitic microstructure, and the other a Dual-Phase DP780 ferritic-martensitic steel. Four plane stress specimen geometries (simple shear, hole tension, v-bend and biaxial Nakazima) were adopted, providing stress triaxiality and Lode parameter values ranging from in-plane shear to biaxial tension under approximately constant stress states until failure. This approach facilitated determination of the relationship between void nucleation and macroscopic stress state. Damage histories were developed from interrupted samples using 3D micro-tomography and quantitative stereology measurement of void nucleation paired with in situ digital image correlation (DIC) strain measurements during the mechanical testing. The trends in damage evolution are strongly linked to the stress state, with very little void nucleation under shear deformation but extensive void damage under biaxial tension for both materials. A dependency of the nucleation rate on Lode parameter was also demonstrated. A higher rate of damage accumulation was observed for the DP780 steel compared to damage in the CP800 steel for all loading conditions highlighting the strong influence of initial microstructure. An analytical framework is proposed to obtain the local stress-state and equivalent plastic strain history from direction integration of the measured DIC strain histories, using a measured hardening law and assumed anisotropic yield function (Yld91) to develop the link between nucleation and the macroscopic stress state. A stress-state dependent nucleation model is proposed by introducing a nucleation strain surface as a function of stress-triaxiality and Lode parameter using a modified form of the strain-based Chu and Needleman nucleation criterion.

Finite element simulations of chip serration in titanium alloy cutting by considering material failure

This paper presents a methodology for simulating serrated chip formation during cutting of alpha-beta ductile titanium alloys. Finite element modelling is combined with material constitutive modelling and ductile failure mechanism that considers failure initiation and cumulative damage evolution to simulate both material separation from workpiece and chip serration mechanisms by applying an elastic-viscoplastic formulation. Failure evolution as function of stress triaxiality is utilized in the simulation. Finite element model is further verified with orthogonal cutting test results by comparing simulated and measured outcomes. Cutting speed and feed effects on chip serration is investigated through the simulation studies. The cutting temperature and strain distributions are obtained to study the chip serration mechanism under different cutting conditions. It is confirmed that the material failure, damage initiation and evolution are of great significance in the chip serration in cutting ductile materials.

Material Testing in Support of the Development and Calibration of Material Models for Forming Simulations

Material testing at various strain rates, temperatures and loading conditions provides data that is used for the development and calibration of constitutive equations (material models) that are utilized in numerical simulations of sheet metal forming. In general, the testing can be divided into characterization tests and validation tests. In characterization tests basic material properties (e.g. yield stress, ultimate stress, failure strain) are determined from a test in which a material coupon is loaded under a well-defined condition (stress, strain rate, temperature, etc.). The data is used for determining the values of parameters in plasticity and failure models. In validation tests a material specimen or a small component is loaded with a more complicated, but well defined, loadings. The test is numerically simulated and the calculated quantities (forces, deformation, failure, temperature, etc.) are compared with measurements. The recent development of the Digital Image Correlation (DIC) technique for full-field measurement of deformation has extended the useful data that can be extracted from traditional characterization tests and provide means for developing new experiments that can be used for obtaining more accurate material models. This paper reviews the advantages of using DIC in traditional tests and presents several new recently developed testing configurations for material coupons and small components. Many of these tests have been used during in the development of a failure surface that gives the equivalent plastic strain to failure as a function of stress triaxiality and the Lode parameter.

Influence of high stress triaxiality on mechanical strength of ASTM A36, ASTM A572 and ASTM A992 steels

This study aims at investigating the influence of high stress triaxiality on the yield strength and ultimate tensile strength of commonly used structural steels (ASTM A36, ASTM A572 and ASTM A992). To this end, axisymmetrically notched steel specimens are designed to generate a range of stress triaxialities. Yield strength and ultimate tensile strength of notched steel specimens are then determined using engineering stress-strain curves obtained from uniaxial tensile testing of notched specimens. Yield strength and ultimate tensile strength of all three types of structural steels are found to increase linearly with increase in stress triaxiality of test specimens. Based on experimental and complimentary finite element results, predictive equations are proposed to estimate increased yield strength and ultimate tensile strength as a function of stress triaxiality in structural steels.

Damage mechanisms in multiphased steels with a bainitic matrix under various mechanical loading paths

Advanced High Strength Steels (AHSS) are frequently used in automotive application to increase passenger safety. These alloys present a good compromise of strength, ductility and toughness. Among these AHSS, the complex phase steel CP1200 is an attractive alloy which exhibits an excellent combination between strength and ductility. The study of its damage mechanisms under various mechanical loadings could help to understand its failure and optimize its formability. Results show a reduction of voids size in function of stress triaxiality. This study highlight that CP1200 presents a high sensitivity to void nucleation mostly located at the ferritic bainite and austenite interfaces.

Experimental and numerical studies of the failure of steel jumpers under snag loads

To limit damage to subsea equipment caused by snag loads, breakaway joints allow failure locations to be strategically defined in the subsea system. A stress modified critical strain (SMCS) failure criterion is used to model the rupture behavior of a notched rigid subsea jumper made from API X65 steel. The jumper is evaluated using finite element analysis when subject to snag loads applied in a given direction. The criterion measures the plastic strain up to failure as a function of stress triaxiality. To verify the accuracy of the failure model, a full scale experimental snag load test is implemented and the resulting snag load-displacement curve is compared with the corresponding finite element simulation. The finite element simulation is observed to predict the experimental load-displacement curve very well up through crack initiation and full breakage at the notched section. Finally, the validated failure model is used in an extensive parametric study of the notch geometry, and design guidance is proposed for an optimally balanced design when consideration is given to snag, fatigue, and operational loading.

Ductile failure modeling and simulations using coupled FE–EFG approach

In the present work, a ductile fracture model has been employed to predict the failure of tensile specimen using coupled finite element–element free Galerkin (FE–EFG) approach. The fracture strain as a function of stress triaxiality has been evaluated by analyzing the notched tensile specimens. In the coupled approach, a small portion of the domain, where severe plastic deformation is expected, is modeled by EFG method whereas the rest of the domain is modeled by FEM to exploit the advantages of both the methods. A ramp function has been used in the interface region to maintain the continuity between FE and EFG domains. The nonlinear material behavior is modeled by von-Mises yield criterion and Hollomon’s power law. An implicit return mapping algorithm is employed for stress equilibrium in the plasticity model. The effect of geometric nonlinearity as a result of large deformation is captured by updated Lagrangian approach. The coupled approach is used to study the fracture behavior of two different cracked specimens in order to highlight its capabilities.

Impact dynamics and puncture failure of pressurized tank cars with fluid–structure interaction: A multiphase modeling approach

This paper presents a computational framework that analyzes the effect of fluid–structure interaction (FSI) on the impact dynamics and puncture failure of pressurized commodity tank cars carrying hazardous materials. Shell (side) impact tests have been conducted on full scale tank cars resulting in deformed or punctured tank cars. A finite element (FE) modeling method is applied that explicitly simulates the three distinct phases in a tank car loaded with a liquefied substance: pressurized gas, pressurized liquid and solid structure. Furthermore, an equivalent plastic strain based fracture initiation criterion expressed as a function of stress triaxiality is adopted to depict the fracture behavior of the tank car steel material. The fracture initiation is implemented for ductile, shear and mixed fracture modes and followed by further material deterioration governed by a strain softening law. The force, displacement and impact energy results obtained from the FE analysis show good agreement with the corresponding shell impact test data. The simulations demonstrate that FSI plays a critical role in predicting the correct dynamics of tank car impact. The puncture resistance of a tank car, characterized as limit impact conditions in terms of puncture energy or puncture velocity, is further analyzed in shell impact scenarios. The puncture energy is shown to increase as the initial fluid pressure decreases, the tank car thickness increases or the effective impactor size increases. Quantitative correlations between puncture energy/velocity and each of these factors are obtained using the FE analysis method developed in this paper.

New Model for Ductile Fracture of Metal Alloys. II: Reverse Loading

AbstractDuctile fracture of metals resulting from large amplitude inelastic reverse straining has been the predominant reason for the failure of structural components under extreme loadings. This kind of fracture, characterized by only a few reverse cycles with large precrack plastic strain, is often termed ultra-low cycle fatigue (ULCF). Ductile failure of metals has recently been recognized to be a function of stress triaxiality and Lode angle parameter. In this paper, a new fracture model with full consideration of stress triaxiality and Lode angle parameter as well as the cutoff regions is proposed from the extension of its equivalence for monotonic loading in the parallel paper. The underlying mechanism and determination of the cutoff region boundary is well-defined and discussed. Additionally, the effect of load excursion on shifting the boundary of the cutoff region and the subsequent damage evolution is assessed. The nonlinearity of damage evolution is also studied and well-characterized. The deve...

Finite Element Modelling of the Progressive Damage and Failure of Thermoplastic Polymers in Puncture Impact

This study analyses the response in puncture impact tests of two types of polymers. Though both investigated materials are polyamide based semi-crystalline thermoplastics, at high strain rates, their behaviour differs as one exhibits ductile behaviour while the other brittle failure. As the investigated materials present high strain-rate dependency, they were modelled with the help of elastic-plastic constitutive laws with rate-dependent plasticity; damage was modelled using ductile and shear damage criteria. The stress-strain response at high strain rates (as puncture impact tests determined rates of deformation up to 200 s-1) and the damage parameters (fracture strain as a function of stress triaxiality and shear stress ratio) were determined and calibrated using finite element analysis simulations through a reverse engineering approach. Simulations performed with the calibrated material models described accurate results in terms of puncture force, puncture energy and failure mechanisms for both investigated polymers.

A model for creep life prediction of thin tube using strain energy density as a function of stress triaxiality under quasi-static loading employing elastic-creep and elastic-plastic-creep deformation

This paper demonstrates the application of a new multiaxial creep damage model developed by authors using stress traixiality to predict the failure time of a component made of 0.5% Cr-0.5% Mo-0.25% V low alloy steel. The model employs strain energy density and assumes that the uniaxial strain energy density of a component can be easily calculated and can be converted to multi-axial strain energy density by multiplying it to a function of stress trixiality which is a ratio of mean stress to equivalent stress. For comparison, an elastic-creep and elastic-plastic-creep FEA analysis is performed to get multi-axial strain energy density of the component which is compared with the calculated strain energy density for both cases. The verification and application of the model are demonstrated by applying it to thin tube for which the experimental data are available. The predicted failure times by the model are compared with the experimental results. The results show that the proposed model is capable of predicting failure times of the component made of the above-mentioned material with an accuracy of 4.0%.

Evaluation of localization and failure of boron alloyed steels with different microstructure compositions

Within the press hardening technology, where hot sheet blanks are simultaneously formed fixed and quenched, new methods with differential thermal treatment come to light. With controlled tool temperature variation, components with tailored properties can be produced. Automotive components combining high energy absorption and intrusion protection in a crash situation are feasible. In the present work the mechanical properties of three different material qualities, beginning with the same base sheet metal subjected to different thermal histories, are investigated. A strategy for modelling post-necking response and crack initiation using shell elements larger then the typical bandwidth of the localized neck is used. The model relies on a sequence of full field measurements throughout a tensile test; i.e. digital speckle photography (DSP). The full field experimental method allows for evaluation of mechanical and failure properties at different analysis lengths, providing parameters for a model which accounts for shell element size. Additionally the model contains a strain based failure criteria as a function of stress triaxiality. Good correlations between a simulated tensile test and experimental results were found. A detailed metallographic study of the three grades was performed and is presented.

A model for creep life prediction of thin tube using strain energy density as a function of stress triaxiality under quasistatic loading employing elastic-creep & elastic-plastic-creep deformation

This paper demonstrates the application of a new multiaxial creep damage model developed by authors using stress traixiality to predict the failure time of a component made of 0.5%Cr-0.5%Mo-0.25%V low alloy steel. The model employs strain energy density and assumes that the uniaxial strain energy density of a component can be easily calculated and can be converted to multi-axial strain energy density by multiplying it to a function of stress trixiality which is a ratio of mean stress to equivalent stress. For comparison, an elastic-creep and elastic-plastic-creep finite element analysis (FEA) is performed to get multi-axial strain energy density of the component which is compared with the calculated strain energy density for both cases. The verification and application of the model are demonstrated by applying it to thin tube for which the experimental data are available. The predicted failure times by the model are compared with the experimental results. The results show that the proposed model is capable of predicting failure times of the component made of the above-mentioned material with an accuracy of 4.0%.

A numerical investigation of spherical void growth in an elastic–plastic continuum

The current work examines the growth of a single void in an elastic–plastic material as a function of stress triaxiality. Using finite volume (FV) stress analysis, growth of a spherical void is simulated and compared to the classic Rice and Tracey model for the different material models considered.

조선 해양 구조물용 강재의 소성 및 파단 특성 II: 파단의 이론적 배경

The main goal of this paper is to provide the theoretical background for the fracture phenomena in marine structural steels. In this paper, various fracture criteria are theoretically investigated: shear failure criteria with constant failure strain and stress triaxiality-dependent failure strain (piecewise failure and Johnson-Cook criteria), forming limit curve failure criterion, micromechanical porosity failure criterion, and continuum damage mechanics failure criterion. It is obvious that stress triaxiality is a very important index to determine the failure phenomenon for ductile materials. Assuming a piecewise failure strain curve as a function of stress triaxiality, the numerical results coincide well with the test results for smooth and notched specimens, where low and high stress triaxialities are observed. Therefore, it is proved that a failure criterion with reliable material constants presents a plastic deformation process, as well as fracture initiation and evolution.