Prediction Of Ductile Fracture Research Articles

Extension of the GISSMO fracture model for thin-walled structures under combined tensile and bending loads

Ductile fracture prediction for thin-walled structures requires computationally efficient simulation tools able to approximately represent the key effects that occur on the sub-thickness scale. Unfortunately, classical shell elements, typically used to model deformation and failure of thin components, are inherently in a state of plane stress and therefore unable to capture the through-thickness stress distribution. This is consequential considering recent studies that demonstrated the differences between fracture in bending vs. in-plane tension. A laterally constrained thin metal plate under in-plane tension is likely to fracture under significantly lower plastic strain than the same plate under bending (with fracture initiating on the tensile side), even though both these conditions are examples of plane strain tension. Under in-plane tension fracture is preceded by a through-thickness neck, and therefore higher stress triaxiality than in the case of plane strain bending, where necking is absent. To account for these differences, we propose an extension of the GISSMO model, which relies on a simple fracture criterion based on stress-dependent fracture strain defined by the user (i.e. fracture locus). The fracture strain is typically determined experimentally using a combination of in-plane tensile tests under varying degree of lateral constraint and shear tests. The proposed extension involves defining a separate fracture locus for bending, also determined experimentally using bending tests. Fracture occurs when the equivalent plastic strain reaches its critical level represented by interpolation between the two bounding cases, i.e. bending and in-plane tension, with a bending index Ω used as an interpolation parameter.

Sequential dual-scale approach for microstructure-informed ductile fracture prediction

This study presents a novel dual-scale finite element method to establish a microstructure-informed ductile fracture criterion for ferrite–martensite dual-phase (DP) steel. At the macroscale, an anisotropic plasticity model with rate-dependent hardening was employed to simulate the material's deformation history. Simultaneously, at the microscale, a dislocation density-based crystal plasticity model was utilized to simulate deformation within a representative volume element (RVE) of the dual-phase steel, constructed using tomography aided by a plasma-focused ion beam/electron backscatter diffraction system.The material properties of the ferrite and martensite phases were determined through X-ray diffraction (XRD) analysis and load-displacement measurements obtained via nanoindentation for each phase. The RVE simulation results were validated against experimentally measured mechanical properties and microstructural changes. The local deformation history at the fracture initiation site, extracted from the macroscale model, was used as boundary conditions for the microscale RVE simulation; sequential dual-scale approach. The models were applied to specimens with varying notch radii, generating different local stress triaxialities and accumulated shear strains at fracture onset. This process allowed the establishment of a ductile fracture criterion, which was further tested in a hole expansion experiment, demonstrating close alignment with experimental data.This sequential dual-scale analysis effectively predicts the deformation behavior of multiphase metallic materials by incorporating realistic microstructures while minimizing computational costs. Consequently, the proposed ductile fracture prediction technique offers a robust method with broad applicability across various metallic materials.

Data-driven void growth prediction of aluminum under monotonic tension using deep learning

Void growth plays a significant role in ductile fracture prediction of aluminum. This study proposes 2 deep learning models to address this issue. For voids that retain their ellipsoidal characteristics during growth, the ellipsoidal void Semiaxes Long Short-Term Memory (SLSTM) method is proposed, using the 3 principal features of the ellipsoid to represent the voids. For voids that undergo arbitrary shape changes during growth, an innovative deep learning method called Voronoi tessellation-assisted LSTM (VLSTM) is proposed. This method uses the Voronoi algorithm to standardize data features and employs Principal Component Analysis (PCA) to perform data compression before neural network training. This new method combines the Voronoi algorithm, LSTM neural networks, and PCA algorithms, and is termed as VLSTM-PCA. In this study the deep learning-based SLSTM surrogate models and VLSTM-PCA surrogate models run approximately 514 and 537 times faster than ABAQUS finite element simulations, significantly enhancing efficiency while maintaining high prediction accuracy. Finally, growth patterns of ellipsoidal voids under different stress triaxialities are analyzed.

Discussion on ultimate resistance formulas of high-strength bolts under tensile-shear coupling loading

Bolted connections are one of the key connection configurations in steel structures. The ductile fracture prediction is one of the challenges in the structural integrity evaluating of steel structures. To guarantee the safety of steel bridge in connections, an accurate assessment of the ultimate resistance of high-strength bolts under combined tensile-shear loads is necessary. However, the impacts of various parameters on high-strength bolts under combined tensile-shear loads are not sufficiently analysed in the existing references. Hence, in this paper, the validated mesoscale critical equivalent plastic strain (MCEPS) method is used to evaluate the ultimate resistance of high-strength bolts with different bolt grades, bolt diameters, bolt types, hole clearance, and preload force when the bolts are exposed to combined tensile-shear loading. The simulation results are compared to existing design specifications. Finally, the formula modifications in the existing design standards are proposed based on statistical analysis on numerical parametric results.

Ductile Fracture Prediction Framework of Low Yield Point Steel LYP225 under Monotonic Loading: Experiment and Simulation

Ductile Fracture Prediction Framework of Low Yield Point Steel LYP225 under Monotonic Loading: Experiment and Simulation

Extended Gurson-Tvergaard-Needleman model considering damage behaviors under reverse loading

Void nucleation, growth, deformation and coalescence are the main microscopic damage mechanisms for plastic deformation of sheet metals. To describe the effect of reverse loading on the microscopic damage accumulation and ductile fracture, the damage evolution equations in regard of void nucleation, void growth, shear void nucleation and shear deformation damage were modified. Through the further introduction of the combined hardening model, an extended Gurson-Tvergaard-Needleman (GTN) model was constructed in this study, to improve the predictive ability of ductile fracture under reverse loading conditions. Two typical reverse loading experiments including compression-tension and shear-reverse shear were performed. The number, size and shape of microscopic voids were qualitatively analyzed and compared through the microscopic observations, it is indicated that the preloading and loading sequence strongly affect the damage accumulation and the final ductile fracture, which is the microscopic damage mechanisms under reverse loading. The proposed GTN model was verified by the load responses and displacements at fracture (DAFs) of the conducted reverse loading experiments. The good agreement between numerical simulations and experimental results proves the rationality of the proposed GTN model and its accuracy to the prediction of ductile fracture under reverse loading conditions.

Ductile fracture prediction of additively manufactured Ti-6Al-4 V alloy based on void growth and coalescence of a unit-cell model

In this work, we have studied the fracture mechanism and proposed a micromechanical method with a unit cell model to predict the ductile fracture of additively manufactured (AMed) Ti-6Al-4 V alloy. The tensile experiments with smooth round bars and notched round bars were conducted to investigate the mechanical properties and ductile fracture behavior of materials. The proposed unit-cell model was validated by quasi-static tensile fracture tests to predict the ductile failure of titanium alloy manufactured by laser power bed fusion (L-PBF) under different stress states, which include a wide range of stress triaxialities. An equivalent initial void fraction was introduced to evaluate the ductile behavior of the titanium alloy. Our investigation shows that the stress states significantly influence the void coalescence behavior of AMed Ti-6Al-4 V alloy, and the fracture locus of L-PBF fabricated Ti-6Al-4 V alloy under different stress states was successfully predicted by the proposed unit-cell model under proportional loading. Our study provides useful guidance for the future design and application of metal materials for additive manufacturing.

Ductile fracture prediction of 7A62 high-strength aluminum alloy under a wide range of stress states

The modified Gurson-Tvergaard-Needleman (GTN) model is employed to predict the ductile fracture of 7A62 high-strength aluminum alloy under a wide range of stress states. Mechanical tests were conducted on specimens with different stress states within the range of −0.33 to 1.35 stress triaxiality, including tension, notched tension, compression, and shear. The results indicate that at high stress triaxialities (0.8 ∼ 1.35), the fracture mechanism is intergranular ductile fracture. Under moderate stress triaxialities (0.33 ∼ 0.8), the fracture mechanism involves a combination of intergranular ductile fracture, void growth, and shear fracture. At low and negative stress triaxialities (−0.33 ∼ 0.33), plastic instability occurs due to uneven stress distribution, leading to shear fracture. Fractography analysis reveals that the fractures occurring under tensile stress are associated with enriched Mn particles of approximately 200 nm. The modified GTN model accurately predicts the load-displacement response, and the fracture paths under various stress states exhibit good consistency with experimental results. This study provides reference for failure prediction in the engineering application of high-strength aluminum alloys.

A review on ductile fracture prediction of cracked/notched components: The distinct and simplifying roles of the equivalent material concept and fictitious material concept

Most of engineering structures and components are made of ductile materials, while fracture mechanics tools have been mostly developed for brittle materials. This article investigates the critical load estimation in fracture problems in presence of the elasto-plasticity from the standpoint of major approaches in fracture mechanics including theoretical, experimental, and computational. A review is comprehensively performed on literature with a main focus on two new concepts, namely the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), by which elastoplastic ductile materials can be simplified to linear elastic brittle materials. Therefore, by overcoming the nonlinear aspects, solving of the fracture problems in the linear elastic fracture mechanics (LEFM) framework becomes possible. It is understood from this comprehensive literature survey that while there are several approaches for estimating ductile fracture in cracked/notched members under various loading conditions, most of them need nonlinear analyses, which are typically time-consuming and complicated. It is shown that EMC can work simply and well on those nonlinear materials having small strain-hardening and small/moderate strain-to-failure, while FMC can be effectively and easily applied to nonlinear materials having moderate/great strain-hardening and/or large strain-to-failure, where failure means necking.

Ductile Fracture Prediction During Metal Forming Using an Ellipsoidal Void Model and Some Other Models

Ductile Fracture Prediction During Metal Forming Using an Ellipsoidal Void Model and Some Other Models

Ductile Fracture Prediction in Hole Hemming of Aluminum and Magnesium Sheets

The present work proposes a suitable approach for predicting ductile fracture in a new joining process by plastic deformation called hole hemming. This process creates a combined form- and force-fit joint and enables the joining of lightweight materials with varying formability without requiring heating or auxiliary elements. In this process, the joinability of materials is limited by the occurrence of fracture in the outer sheet, highlighting the crucial need to accurately predict its damage during the process design phase. In this study, five different fracture criteria, including the McClintock, Rice–Tracey, Normalized Cockroft–Latham, and Brozzo and Modified Mohr–Coulomb (MMC) criteria, are examined during the joining of a challenging combination of lightweight materials (aluminum AA6082-T4 and magnesium AZ31). These criteria are calibrated by a hybrid experimental–numerical method using three tests with distinct stress states. These criteria are then implemented into the finite element model of the hole hemming process, utilizing an appropriate user subroutine. The results show that the flange edge of the outer sheet is the most prone region to fracture during the joining process, and a criterion must be able to model the fracture behavior of the material from uniaxial tension to shear to accurately predict fracture in this area. Among the examined criteria, only the MMC criterion was capable of such modeling and accurately predicted the critical displacement of the punch in the hemming stage with a negligible error (about 1%). On the other hand, the prediction accuracy of the other criteria varied significantly depending on the calibration test, resulting in errors ranging from 8.6% to 75.5%. The error of 8.6% was achieved with the Normalized Cockroft–Latham criterion calibrated by a uniaxial tension test. Thus, based on the results, the MMC criterion is recommended for ductile fracture prediction in the hole hemming process, offering valuable insights to assist in process design.

Ductile fracture prediction of HPDC aluminum alloy based on a shear-modified GTN damage model

In this paper, we investigate how the shear-modified Gurson-Tvergaard-Needleman (GTN) model can be used to reveal the effect of manufacturing-process-induced porosity on the scatter of ductile fracture properties of a high-pressure die-casting aluminum alloy. The GTN model exhibits great advantages in predicting the variation of failure strain/displacement by altering the initial void volume fraction (f0), compared with uncoupled ductile damage models. For a specific metallic material, one unique set of model parameters is usually determined from experiments, which leads to the fact that only a deterministic failure strain/displacement can be obtained under a fixed porosity. To overcome this shortcoming of the shear-modified GTN model, a novel parameter calibration scheme is proposed and validated in the present study. Following the physical background of the GTN model, the twelve material parameters of the shear-modified GTN model have been determined based on a combination of macroscopic mechanical tests covering a wide range of stress states and micromechanics-based unit cell simulations. Different from the existing calibration strategies, the simulation results of unit cells embedded with a spherical void have revealed a mutual dependence between the f0 and critical void volume fraction (fc). By conducting interrupted shear tests, the evolution of secondary nucleated void volume fraction was identified according to the statistical results of the fractured brittle silicon particles. The remaining parameters have been further iteratively determined. In the end, the effectiveness of the proposed parameter determination approach is confirmed based on the accurate prediction of stochastic ductile failure properties (both the global failure displacements and the local failure patterns) in different fracture tests. Given the proposed parameters identification strategy, the GTN material models have been enriched to predict the ductile failure behavior of metallic materials, which possess relatively high porosities and more pronounced scattering in failure properties.

Flow stress curves for 980MPa- and 1.5GPa-class ultra-high-strength steel sheets weakened under high-stress triaxiality

The weakening behavior of ultra-high-strength steel(UHSS) remains unknown, even though it is a requirement for the accurate prediction of strain localization and ductile fracture in automobile applications. In this study, we, therefore, revealed the stress–strain curves of UHSSs up to their ductile fracture under different stress triaxialities for the first time. Smooth and notched tiny round-bar specimens cut from UHSSs with 1.6 mm thickness were subjected to tensile tests, during which the forces and neck diameters of the specimens were measured. Notably, the evaluated flow stresses in the 1.5 GPa-class notched UHSS specimens exhibited weakening of up to 3%. This was in contrast to the 980 MPa-class UHSS specimens, which did not exhibit notch-induced weakening. The absence of weakening during stress measurements, as confirmed by synchrotron X-ray diffraction (XRD) analysis, suggested that weakening was caused by material damage. However, the weakening behavior did not follow the previously developed damage models based on microvoid formation. The volume fraction of the microvoids, as observed by X-ray computer tomography, was extremely small (at 0.2%) and cannot account for the 3% material weakening indicated by the flow stress measurement results. A new damage mechanism, associated with unobservable small lattice vacancies, was implied in UHSSs deformation under high stress triaxialities.

Accurate numerical prediction of ductile fracture and micromechanical damage evolution for Ti6Al4V alloy

Accurate numerical prediction of ductile fracture and micromechanical damage evolution for Ti6Al4V alloy

The modified GTN model for fracture of nickel-based superalloys considering size effect and healing effect in pulsed current assisted deformation

Gurson-Tvergaard-Needleman (GTN) model is one of the most famous and classical criterions widely used in modelling the ductile fracture process of metal. However, the existence of grain size effect affects the ductile fracture prediction in micro-scaled plastic deformation of nickel-based superalloy ultrathin sheet. In the pulsed current assisted (Pca) forming process, the current has a healing effect on the micro-void of metal due to the existence of local Joule heat, yet the strain has a promotion on the micro-void growth, and the coupled effect between grain size and electrical field is complicated, which makes it difficult to predict the fracture for the traditional GTN model in Pca forming process. To solve this problem, the authors added pulsed current parameters to the GTN model to describe the healing effect of pulsed current on the voids in the material. The parameters of the GTN model were calibrated by the finite element inverse identification method. The modified GTN model was embedded into Abaqus by VUMAT, and the Backward Euler algorithm was employed to integrate the constitutive equation. The validity of the model was verified by comparing the true stress-strain curves with the simulation results and comparing the void volume fraction (VVF) measured by three-dimensional X-ray computerized tomography (3DCT). The model provides a new method for ductile fracture prediction of multiphase alloys under a discontinuous energy field. Meanwhile, it is confirmed that the behaviour of fracture and necking in the Pca forming process is affected by the coupling effect of pulsed current and grain size effect, which provides a new idea for studying the Pca forming process.

Hardening Behavior and Prediction of Ductile Fracture during AA7075-T651 Sheet Metal Forming

Hardening Behavior and Prediction of Ductile Fracture during AA7075-T651 Sheet Metal Forming

A Compensation Algorithm for Large Element Characterizing the Damage Evolution Process and Its Application to Structure Collisions

When simulating the process from elastic–plastic deformation, damage to failure in a metal structure collision, it is necessary to use the large shell element due to the calculation efficiency, but this would affect the accuracy of damage evolution simulation. The compensation algorithm adjusting failure strain according to element size is usually used in the damage model to deal with the problem. In this paper, a new nonlinear compensation algorithm between failure strain and element size was proposed, which was incorporated in the damage model GISSMO (Generalized incremental stress state dependent damage model) to characterize ductile fracture. And associated material parameters were calibrated based on tensile experiments of aluminum alloy specimens with notches. Simulation and experimental results show that the new compensation algorithm significantly reduces the dependence of element size compared with the constant failure strain model and the damage model with the linear compensation algorithm. During the axial splitting process of a circular tubular structure, the new compensation algorithm keeps the failure prediction errors low over the stress states ranging from shear to biaxial tension, and achieves the objective prediction of the damage evolution process. This study demonstrates how the compensation algorithm resolves the contradiction between large element size and fracture prediction accuracy, and this facilitates the use of the damage model in ductile fracture prediction for engineering structures.

Stress-state-dependency of post-necking hardening rule and its influence on ductile fracture prediction

This paper presents the investigation of the stress-state-dependency of the post-necking hardening rule of the Q355B structural steel and its influence on fracture prediction. The comparisons of the testing result and the simulation based on the Mises model with the stress-state-independent hardening rule indicate that triaxiality dependency under axisymmetric tension is negligible, while the reduced yield stress increases with the rising triaxiality under plane strain. In addition, the overestimated predicted force based on the Mises model is continuously ramping up along with the plastic deformation under the shear-dominant condition. It can be considered by the reduced post-necking hardening rate under the requirement of convexity of the yield surface. The stress-state-dependent hardening model (SDH model) is herein proposed including the modified triaxiality-dependent Hosford yield criterion and state-dependent post-necking hardening rule. The comparative studies of the proposed and conventional models show similar calculated fracture strains under high triaxiality, but considerably larger fracture strain under low triaxiality from the proposed SDH model, since the reduced post-necking hardening rate intensifies the localization of plastic deformation. Using the proposed pressure-dependent maximum shear stress (PMSS) fracture model, the calibrated fracture parameters based on the data from SDH the model produce better fracture simulations under various stress states, especially the complex condition in multi-hole plate (MHP) specimen. It emphasizes the necessity of the consideration of stress-state-dependency in the post-necking hardening rule for accurate fracture prediction.

Ductile fracture prediction of ZK61M high-strength magnesium alloy sheet during hot deformation process

To predict the ductile fracture behavior of a ZK61M high-strength magnesium alloy sheet during hot deformation, experiments and numerical simulations were performed under specific conditions. According to the stress state parameters and fracture strain data obtained for different specimens, the undetermined coefficients of four fracture models were solved using the particle swarm optimization algorithm. According to the error evaluation results, the modified Wilkins model was the most accurate. This model was introduced into a finite element, and the results were compared with experimental results. The results indicated that the mean relative errors of the fracture displacement and fracture load of the tensile parts were <15%, and the mean relative error of the forming depth of the cylindrical parts was 13.88%. The established finite element model can accurately simulate the experimental process and predict the fracture position.

Analysis of ultimate fracture bearing capacity of CHS XK-joints welds

The current study presents advanced finite element (FE) models that combine the stress weighted damage model and the crack propagation using explicit dynamic approach of commercial FE software ABAQUS. The applicability of the subroutine for ductile fracture prediction and crack propagation modeling of structural steel is confirmed by comparing the results of fracture tests performed on circumferential notch specimens. FE analysis is performed on 17 circular hollow section (CHS) XK-joint models with various sized partial penetration welds to simulate the fracture process of the joint models, and the obtained results are used to analyze the fracture ultimate bearing capacity of the joint weld. The results indicate that the crack first appears on the inner side of the weld at the crown point of the intersecting line of the tensile web member. The findings also demonstrate that the joint weld does not lose the bearing capacity completely after the initial cracking. Instead, the joint weld's bearing capacity increased with the displacement at the early stages of fracture propagation to reach the maximum value prior to gradual decrease in bearing capacity. A design formula of weld bearing capacity suitable for partial penetration weld has been proposed herein to incorporate the effects of uneven distribution of joint weld stress in the considered XK-joints.