Ductile Fracture Criterion Research Articles

Design of flat hole-clinching for joining polymer and metal sheets

There is a growing need for joining processes capable of joining dissimilar materials, specifically lightweight materials. In this study, flat hole-clinching (FHC) is developed for joining polycarbonate and AZ31 magnesium alloy sheets. A ductile fracture criterion is calibrated using tensile tests and employed in the finite element analysis of the process to investigate the effect of geometric parameters on the joint characteristics and strength. A tool concept is also proposed for the FHC process. Results show that the FHC process enables to successfully connect these sheets without fracture. The flat hole-clinched joint resisted the maximum force of 0.9 kN in the pull-out test, and failed with bottom separation mode.

A data-driven ductile fracture criterion for high-speed impact

Data-driven methods based on machine learning (ML) models offer new approaches for characterizing the fracture behavior of advanced elastoplastic materials. In this paper, a ML-based data-driven ductile fracture criterion is proposed to characterize the fracture behavior of elastoplastic materials under high-speed impact loading conditions. To reduce the required training dataset and enhance the predictability capability, several assumptions are used. Firstly, utilizing the decoupled assumption, two separate artificial neural network (ANN) models are employed to establish the fundamental fracture model and characterize the strain rate effect of ductile fracture behavior, respectively. In addition, the enhanced method with a logarithmic function is introduced to improve predictability capability of the proposed data-driven criterion under unknown high strain rates. To establish a complete numerical implementation framework, an enhanced rate-dependent data-driven constitutive model and a compatible numerical implementation algorithm are additionally introduced. Eventually, to assess the applicability of the proposed data-driven fracture criterion, numerical simulations of notched specimens and ballistic impact conditions of Ti-6Al-4V material are conducted, respectively. These investigation results demonstrate the effectiveness of the proposed data-driven ductile fracture criterion.

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.

Size Effect on the Ductile Fracture of the Aluminium Alloy 2024-T351

BackgroundReliably calibrated criteria are needed for an accurate prediction of fracture of various components. However, there is not always a sufficient amount of material available. Therefore, miniature testing provides an alternative that is researched together with the following calibration of the ductile fracture criteria and investigating the size effect.ObjectiveThe aim is to design miniature testing equipment and specimens for tensile testing, which covers various stress states. This is supplemented by the small punch test, which has the same specimen thickness, taken from the literature to broaden the portfolio for calibration. The second part deals with conducting the finite element analysis, which provided a basis for the calibration of the phenomenological ductile fracture criterion applicable to crack-free bodies to indicate the crack initiation.MethodsThe steel frame to test thin specimens is designed with optical measurement of deformations. The finite element method is used, within Abaqus and user subroutines, to simulate the tests to obtain the variables needed for the calibration. In addition, the calibration of the criterion using machine learning is explored.ResultsThe feasibility of the proposed experimental program is tested on the aluminium alloy 2024-T351. Moreover, the numerical simulations, which showed a good match with experiments in terms of force responses, adds to the knowledge of modelling in the scope of continuum damage mechanics.ConclusionsThe presented results provide a material basis for the aluminium alloy studied on a lower scale, while they broaden the testing possibilities and analyses the calibration strategies for the best failure predictability possible.

An uncoupled ductile fracture criterion for a wide range of stress states in sheet metal forming failure prediction

In industrial production, sheet metal rupture will inevitably occur in the process of forming, especially in the shape of complex, relatively small thickness of the sheet. It is vital to accurately predict the failure of ductile metals under various working conditions. To deal with the problem, an uncoupled ductile fracture criterion (DFC) for a broad range of stress states is proposed based on the micro-mechanism of ductile fracture of metals, which redefines the relationship between the number of void nucleating and the equivalent plastic strain and takes into account the different deformation modes of the voids in the growth stage. Then, in order to verify the validity and advantages of the proposed DFC, the 3D fracture surface of AA 2024-T351 and AISI 1045 steel are constructed by the new criterion based on their fracture data under various stress states, and compared with the commonly used DF2016 criterion and Hu criterion. The prediction results show that the new criterion is better than them, both in terms of the maximum prediction error and the average prediction error. Furthermore, to further prove the effectiveness of the proposed model, five samples are designed for tension tests to calibrate the new DFC using a hybrid experimental–numerical approach, and the calibrated criterion is applied to cupping simulations of AA 6061 and compared with cupping experimental results. The results indicate that the Erichsen cupping number (IE) of the cupping simulation and experiment are 6.88 mm and 7.05 mm, respectively, and the error between them is only 2.411 %, and the location of the fracture is also basically the same. Therefore, all comparison results show that the proposed DFC can forecast the fracture problem in sheet forming more accurately under various stress states.

A strain components-based Mohr–Coulomb fracture criterion for proportional loading

Ductile fracture criteria are crucial in the application of elastoplastic materials like advanced high-strength steels, particularly due to their tendency to fail without significant localized necking. It is aimed to figure out the unified mechanism for ductile fracture and accurately describe it with phenomenological criteria. In this study, the effect of the stress triaxiality and the Lode parameter is analyzed mathematically. The maximum shear strain and the normal strain to fracture are emphasized in the proposed strain components-based Mohr–Coulomb fracture criterion particularly designed for plane stress states, and it is assumed that fracture occurs when the combination of the maximum shear strain and the normal strain reaches the critical value. It is then extended to describe fracture with the equivalent plastic strain and the normal strain to fracture. The experimental fracture data of AA 2024-T351 and the additively manufactured Ti-6Al-4V titanium alloy are used to verify the proposed models. A fracture forming limit diagram comprising forming limit curves calibrated from stress states under different stress triaxialities is proposed based on the proposed fracture criteria for plane stress states. This study shows that a strong correlation between the maximum shear strain and the normal strain to fracture has been observed, and it can be described piecewise-linearly. Besides, the orientation of the fracture surface under both tension (including plane strain tension) and compression (including plane strain compression) can be qualitatively explained by the Mohr’s strain circles. The results provide a new insight into the intrinsic deformation and fracture mechanism of materials that fail without severe localized necking.

Microstructure-Based Modeling of Deformation and Damage Behavior of Extruded and Additively Manufactured 316L Stainless Steels.

In this study, we investigated the micromechanical deformation and damage behavior of commercially extruded and additively manufactured 316L stainless steels (AMed SS316L) by combining experimental examinations and crystal plasticity modeling. The AMed alloy was fabricated using the laser powder bed fusion (LPBF) technique with an orthogonal scanning strategy to control the directionality of the as-fabricated material. Optical microscopy and electron backscatter diffraction measurements revealed distinct grain morphologies and crystallographic textures in the two alloys. Uniaxial tensile test results suggested that the LPBFed alloy exhibited an increased yield strength, reduced elongation, and comparable ultimate tensile strength in comparison to those of the extruded alloy. A microstructure-based crystal plasticity model was developed to simulate the micromechanical deformation behavior of the alloys using representative volume elements based on realistic microstructures. A ductile fracture criterion based on the microscopically dissipated plastic energy on a slip system was adopted to predict the microscopic damage accumulation of the alloys during plastic deformation. The developed model could accurately predict the stress-strain behavior and evolution of the crystallographic textures in both the alloys. We reveal that the increased yield strength in the LPBFed alloy, compared to that in the extruded alloy, is attributed to the higher as-manufactured dislocation density and the cellular subgrain structure, resulting in a reduced elongation. The presence of annealing twins and favorable texture in the extruded alloy contributed to its excellent elongation, along with a higher hardening rate owing to twin-dislocation interactions during plastic deformation. Moreover, the grain morphology and defect state (e.g., dislocations and twins) in the initial state can significantly affect strain localization and damage accumulation in alloys.

Investigating the formability of 6061-T6 aluminum alloy sheets at elevated temperatures using experimental and numerical methods

The high weight-to-strength ratio of AA6061 aluminum alloys presents increased potential applications in industries such as automotive and aircraft. However, its limited formability at room temperature (RT) restricts its usage. Therefore, in the conducted study, the formability of AA6061-T6 sheets with a thickness of 2 mm was investigated at different temperatures in the range of RT up to 300°C. Both experimental and numerical methods were employed to investigate the forming limit diagram (FLD) of an AA6061-T6 sheet. The tests were conducted using a non-isothermal Nakajima standard die under dry contact conditions. Two damage criteria, the Johnson–Cook and the ductile fracture criterion (DFC), were used in a thermomechanically coupled finite element analysis in Abaqus/Explicit to predict fracture in the AA6061 sheet. To examine the impact of temperature on the friction coefficient in the punch and sheet contact, an atomic force microscope was used to measure the roughness of the sheet, after the FLD tests, were conducted at different temperatures. Results indicate an increase in FLD levels from RT up to 100°C, followed by a decrease, for temperatures surpassing 100°C. Experimental findings underscored the significance of the adhesive wear at elevated temperatures, acting as a decisive factor that hampers the material flow and the sheet deformation, in the contact between the sheet and punch.

Study on Plastic Constitutive Relation and Ductile Fracture Criterion of AM60B Magnesium Alloy.

It is currently a challenge to accurately predict the deformation and fracture behavior of metal parts in automobile crashes. Many studies have shown that the deformation and fracture behavior of materials are significantly affected by the stress state during automobile crashes with complex stress state characteristics. In order to further promote the application of die-cast magnesium alloys in automobiles, it is particularly important to study the material deformation and fracture behavior of die-cast magnesium alloys. In this paper, the mechanical properties of the AM60B die-cast magnesium alloy sheet under four stress states (shear, tension, R10 notch tension, and cupping) were designed and tested. Based on the von Mises isotropic constitutive model and Swift weighted Hockett-Sherby hardening model, the plastic constitutive model of die-cast magnesium alloy was established. Based on the plastic model and the fracture model (JC, MMC, and DIEM) considering the influence of three stress states, the deformation and fracture behavior of the AM60B die-cast magnesium alloy front-end members in three-point bending were predicted by experiments and finite element simulation. The experimental results show that the deformation mode and loading-displacement curve trend of the AM60B die-cast magnesium alloy front members are the same, the crack initiation point and crack initiation time are the same, and the crack shape is similar. The results show that the complex stress state constitutive model parameters and the DIEM fracture model obtained in this paper can accurately predict the deformation and fracture failure behavior of the AM60B die-cast magnesium alloy sheet.

Anisotropic ductile fracture of a stainless steel under biaxial loading: Experiments and predictions

The anisotropic ductile fracture behavior of a stainless steel is investigated using a combination of experiments and analysis. The material is SS-304L, an austenitic, low-carbon stainless steel, received in the form of tubes of 2.38 mm dia. and 0.15 mm thickness. The tubes are inflated under volume control in a custom apparatus. At the same time, the axial force on the tubes is kept proportional to the pressure induced by the inflation. This leads to quasi-proportional stress paths in the meridional-hoop engineering stress space. A total of 15 discrete paths are successfully tested. Stereo-type Digital Image Correlation is used to measure the strains. In every case, the tubes develop a series of instabilities before bursting. The failure is oriented along the meridional or the hoop direction of the tube, depending on which stress is greater. A mild plastic anisotropy is detected in these experiments. Hence these results are then used for calibrating the anisotropic yield criterion Yld2004-3D. This is introduced in a finite element model of the experiments, which includes a thickness imperfection designed to capture the two failure orientations observed in the experiments. The numerical model using the Yld2004-3D criterion reproduces the experiments well, e.g., it captures the experimental stress-strain and induced strain paths better than von Mises. It is then used to probe the conditions at the onset of fracture (hybrid method). It is found that most paths lead to essentially proportional loading during deformation. A significant anisotropy in the fracture behavior is detected, with the meridional-stress-dominated paths being able to develop much higher strains than the hoop-dominated ones. These results are then captured by the DF2016 ductile fracture criterion, modified to use the anisotropic yield criterion Yld91. The proposed criterion is flexible enough to represent the fracture anisotropy very well, without being unnecessarily complex. The fracture forming limit curve (i.e., the fracture envelope in strain space) predicted by the DF2016/Yld91 model is also found to be very close to the experiments. The results and findings of this work help establish a framework to reliably design components and processes when significant fracture anisotropy is expected.

Assessment of the possibility of quantitative identification of the Mannesmann effect using ductile fracture criteria

AbstractThis article presents a study to estimate the possibility of determining the shape and size of a Mannesmann effect crack using the finite element method. Experimental tests were carried out to obtain reference specimens with a crack. A rotational compression test of cylindrical specimens in a channel was used for the experimental studies. Finite element tests were carried out using nine ductile fracture criteria. In the first stage of the study, using the rotational compression test and the finite element method, the limit values of the fracture criteria were determined. In the second stage, the development of a Mannesmann effect crack was simulated using the limit values of the fracture criteria using the finite element method. Based on the analysis, it was found that the greatest agreement in terms of void shape and size obtained in finite element method and experiment was obtained for the Ayada criterion. Analysis of the progression of the shape of the void formed using the Ayada criterion showed that crack initiation occurs as a result of maximum principal stress. The development of the resulting void is the result of the action of the maximum shear stress as well as the maximum principal stress.

Numerical Investigation of the Evolving Inelastic Deformation Path of a Solder Ball Joint under Various Loading Conditions

Solder joints of ball grid arrays (BGA) have been widely used to connect electronic components to printed circuit boards (PCBs) and are often subjected to mechanical stress. Several studies have been conducted on the mechanical reliability of solder joints. While these studies have been useful in the industry, detailed studies on how the inelastic deformation path of the solder ball joints evolves under specific loading conditions have not been sufficiently reported. This study aims to understand how the inelastic deformation path evolves when a solder joint is subjected to a constant external force by utilizing the theory of mechanics. It has also been found that the mechanical failure is strongly influenced by the evolution history of the deformation modes in materials. For this study, an elastoplastic constitutive model and a ductile fracture criterion were implemented into the vectorized user-defined material (VUMAT) subroutine of the ABAQUS program for finite element (FE) analysis. With the model, the evolution of the inelastic deformation path of a single solder ball under different loading conditions was numerically analyzed. Three loadings (shear, compression, and bending) were chosen as the basic loading conditions. In addition, combinations of the basic loadings resulted in three dual loadings and one complex loading. The simulation results showed that the shear and bending caused the fracture for both single and dual loadings, but when combined with compression, the fracture was suppressed. The results indicate that fracture is not solely determined by the magnitude of equivalent plastic strain but also by the evolution of inelastic deformation mode. This research offers an improved understanding of the significance of the inelastic deformation path and fracture.

Simulation-Free Identification of the Reduced Hosford–Coulomb Ductile Fracture Criterion for Nimonic Sheets Assisted by the Virtual Fields Method

Simulation-Free Identification of the Reduced Hosford–Coulomb Ductile Fracture Criterion for Nimonic Sheets Assisted by the Virtual Fields Method

Prediction of forming limit for sheet metals between equi-biaxial tension and uniaxial tension using a new ductile fracture criterion

Prediction of forming limit for sheet metals between equi-biaxial tension and uniaxial tension using a new ductile fracture criterion

Multi-scale numerical investigation of deep drawing of 6K21 aluminum alloy by crystal plasticity and a stress-invariant based anisotropic yield function under non-associated flow rule

In this research, the earing characteristics of 6K21 aluminum alloy in circular cup deep drawing are investigated by virtue of experiments and multi-scale simulations including anisotropic Drucker, Hill48, Yld91 yield functions and crystal plastic finite element model (CPFEM). First, the deep drawing experiments of AA 6K21 are carried out to explore the influences of blank holding force (BHF) and blank diameter (BD) on earing profile and mechanical response. The user-defined material model subroutine is written for LS-DYNA explicit code, including constitutive model and ductile fracture criterion under associated or non-associated flow rule (NAFR). The parameters of the crystal plasticity model are calibrated by means of an optimization algorithm. Three yield functions under NAFR and CPFEM are used to predict earing in deep drawing simulation. The effects of five textures on the earing profiles and thickness variables are studied by CPFEM. The results demonstrate that the earing rate decreases slightly as the BHF increases. However, the mechanical response changes insignificantly. Moreover, as the BD increases, both the earing rate and mechanical response increase significantly. Considering computation accuracy and efficiency, the anisotropic Drucker function can accurately character the plastic deformation behavior of deep drawing. For five textures in CPFEM, Cube and Goss textures produce four ears at 0o and 90o from the rolling direction. Brass and S textures form six ears at 0o and 55o. Copper texture fabricates eight ears at 40o and 70o. The influences of five textures on earing rate are Goss > Cube > Copper > Brass > S. Furthermore, there are obvious thickness gradient fluctuations at the corner of the cup in Cube, Goss and Copper textures. It is expected to reduce the earing rate and improve the formability through reasonable allocations of experimental parameters and texture proportions.

Ductile fracture behavior of in situ TiB2 particle reinforced 7075 aluminum matrix composite in various stress states

The fracture behavior of an in situ TiB2 particle reinforced 7075 aluminum matrix composite in various stress states was investigated by mechanical tests, microscopic characterization, and numerical simulations. Four sets of tensile specimens, one group of shear specimens, and one group of compression specimens were designed, and mechanical experiments were conducted on these six groups of specimens. The strain distributions of the six groups of specimens during deformation were investigated by in situ strain testing and finite element simulation. The fracture morphology of the specimens was characterized to analyze the damage mechanism in different stress states. It was found that the fracture mechanism of the material is mainly interfacial debonding and particle fracture, manifested as tensile fracture under high stress triaxiality and shear fracture under low stress triaxiality. For the tensile fracture, the nucleated voids grew with the maximum principal stress; for the shear fracture, they showed significant shape change with the maximum shear stress but little volume change. Based on the fracture mechanisms uncovered by the experiments, a modified ductile fracture criterion, considering the influence of both the maximum principal stress and maximum shear stress, was developed for the composite. Comparison with the modified Mohr–Coulomb, Lou–Yoon–Huh, Hu, and Mu models shows that the proposed model can predict the ductile fracture behavior of the aluminum matrix composites more accurately.

In-situ EBSD observation and simulation of free surface roughening and ductile failure in the ultra-thin ferritic stainless steel sheet

Surface roughening is one of the most fundamental issues which greatly affects the plastic deformation and ductile fracture behavior of ultra-thin sheet materials. The present study investigated the influence of free surface roughening on the micromechanical failure in the ultra-thin ferritic stainless steel (FSS) sheet for bipolar plate in proton exchange membrane (PEM) fuel cell under in-situ tensile deformation. The microstructural evolution during uniaxial tension was monitored using in-situ electron backscatter diffraction (EBSD) technique. Then the initial microstructure was directly mapped onto the finite element mesh of representative volume element (RVE) in the crystal plasticity finite element (CPFE) simulation. The CPFE model was incorporated with the microscopic ductile fracture criterion in terms of plastic energy dissipation in order to simulate the initiation of ductile fracture caused by the free surface roughening. The in-situ EBSD observations reveal that the microstructure of the ultra-thin FSS sheet exhibits heterogeneous plastic deformation and strain localization on the surface at the large deformation owing to the considerable free surface roughening. The CPFE simulations well reproduce the stress/strain heterogeneity and the local hotspots of the ductile fracture initiation. It reveals that the increase of surface roughness with the deformation results in the increased inhomogeneity of thickness which accelerates the strain localization, consequently the premature necking and failure in the ultra-thin steel sheet. Due to the free surface roughening which can facilitate strain localization, the initiation of ductile fracture is obviously observed in both the ridges and valleys in the free surface and its propagation along the pronounced localization band through the thickness, leading to material failure. The good correlation of free surface roughening to the onset of plastic instability and ductile fracture further advances the insight into the micromechanical failure during plastic deformation of the ultra-thin FSS sheet for bipolar plate in PEM fuel cell.

Predicting the forming limits in the tube hydroforming process by coupling the cyclic plasticity model with ductile fracture criteria

This study presents a one-surface plasticity constitutive model combined with phenomenological and micromechanical damage models to be applied to the large plastic deformation during tube hydroforming. These factors lead to simulating the Bauschinger effect and transient behavior in large plastic strain ranges and predicting fracture onset. By using the integration approach, a numerical integration algorithm of implementation by explicit schemes was carried out. A comparison of several cyclic loading tests between experiments and numerical simulation was accomplished. The accuracy of these models is verified, which could be expanded to a large strain range forming process. Adopting the proposed models, finite element modeling is performed in the tube hydroforming process. The simulation and experimental results comparison showed that the proposed framework accurately predicted the tube formability in the hydroforming process.

Computational prediction of chevron cracking during multi-pass cold forward extrusion

The cold forward extrusion is a manufacturing process that is widespread in automated production due to its economic benefits. The cross-section is reduced during this process, which is accompanied by large plastic deformations. It may lead to the chevron cracking, which has to be predicted for flawless production and maintaining economic advantage. Therefore, the multi-pass cold forward extrusion of cylinder made from AISI 1045 was numerically simulated. The central cracks were predicted by the recently proposed uncoupled ductile fracture criteria. These were calibrated using various experiments, including the small punch test with additional fractographic observation. The material model was implemented into Abaqus using the user subroutine so that defects were successfully predicted using an element deletion technique.

Studies on resistance behavior of modified blind-bolts under pure tension and shear

Blind-bolts offer a feasible way for connecting a steel member with closed-hollow section to a member with open-section. However, the relatively higher cost of the available blind-bolts is an obstacle to practical application. For reducing the production cost, a modified Hollo-Bolt with standardized slotted sleeves (MBB) was proposed. To investigate the load-resisting behavior of the proposed MBB and conduct comparative studies with the normal blind-bolt (NBB), extensive experimental tests under pure tension and shear were performed on NBB and MBB of three different diameters and two common strength grades. The results indicate that MBBs and NBBs showed similar load-resisting behavior under tension as the fracture strength of the bolt shank solely controlled the ultimate tension-resisting capacity of the blind-bolt unit. Under simple shear, however, the load-resisting capacity of MBBs was slightly lower than that of NBBs due to the relatively shorter embedment length of its unslotted tube. Nonetheless, the load-resisting capacities of both MBBs and NBBs under simple shear were significantly higher than those of common high strength bolts, owing to contributions from the sleeve and unslotted tube. Moreover, finite element models incorporating ductile fracture criterion were established to replicate the load-resisting behavior of the blind-bolts under tested scenarios. It was revealed that the differences in the shear resistance of NBB and MBB were mainly attributable to the significant tensile stress of the bolt shank and the delayed damage of unslotted tube, which is essentially related to the embedment length of unslotted tube.