Fracture Forming Limit Research Articles

Fracture forming limit curve prediction by ductile fracture models

The fracture forming limit curve is an essential tool giving information about fracture initiation in metal forming applications. In order to obtain a fracture-forming limit curve, the Nakajima test should be carried out. However, these tests are costly and time-consuming processes. Therefore, companies in the automotive industry tended to use non-expensive numerical approaches to determine the material's formability limits. In this work, an anisotropic polynomial yield criterion was implemented to calibrate the different ductile fracture models, including only or both the stress triaxiality and the Lode parameter's effect. Analyses of different uniaxial tensile test geometries were carried out, and the two-dimensional fracture loci were constructed by different ductile fracture models. Correspondingly, the fracture-forming limit curves were predicted by the two-dimensional fracture loci. The results showed that the ductile fracture models, including only the stress triaxiality effect, provide an acceptable performance covering the range from uniaxial tension and the plane strain tension lines, while the models, including the stress triaxiality and Lode parameter, provide a plausible prediction performance throughout the whole range for forming limit diagram.

EFFECT OF ARB PROCESS ON WEAR RESISTANCE, PLAN STRESS FRACTURE TOUGHNESS AND FORMING LIMIT DIAGRAMS OF LAMINATED Al/SiC COMPOSITES

In this study, liquid casting process is used to fabricate AA1050/SiC composites. To increase the wettability of molten Al and improve the adhesion of particles to metallic matrix, liquid casting was selected as the fabrication process. AA1050 and Nano-SiC particles were selected as metallic matrix and reinforcements, respectively. Then, wear, mechanical properties, fracture toughness and forming limit diagram of (FLD) of aluminum composite samples have been investigated experimentally. To do this, AA1050/SiC composite strips with thickness of 1 mm have been fabricated up to eight ARB passes at 300∘C. The graining was investigated via optical microscopy (OM). The ultimate tensile strength (UTS) of samples improved to 170 MPa registering 168% improvement than the initial monolithic sample. Also, the bonding quality among the layers improved by decreasing the thickness of layers at higher number of passes (increasing the plastic strain). SEM fracture surface morphology of samples after the tensile test showed that by increasing the ARB passes, shear ductile was the fracture mode. So, deep dimples are shrinking slowly relative to the annealed sample. The FLDs’ area dropped sharply for pass 1 and then improved at higher passes as the criterion of formability. Also, wear resistance of composite samples was better than monolithic sample. Moreover, at the 10th pass, the fracture toughness enhanced to the maximum value of 33.5 MPam[Formula: see text].

Fracture Prediction of Aluminum Alloy Sheet AA2024-T3 Using Analytical Stress and Experimental Strain Based Failure Criteria

In this work, the fracture prediction of aluminium alloy sheet, grade AA2024-T3 was investigated using the Fracture Forming Limit Curve (FFLC) and Analytical Fracture Forming Limit Stress Curve (FFLSC) as failure criteria. Initially, the FFLC was experimentally achieved by means of the Nakajima Stretch forming test coupled with GOM strain measurement system, providing the Digital Image Correlation (DIC) technique. Subsequently, the analytical FFLSC was plastically computed using experimental FFLC data combination with Swift hardening model and anisotropic Hill’48 yield model for representing anisotropic plastic deformation behaviour on examined sheet. Finally, Fukui stretch drawing and Three point bending tests were conducted both experiment and numerical simulation to evaluate the fracture state and verifying an applicability of obtained FFLC and FFLSC. In the simulation, the ABAQUS 2017 element deletion function was employed for directly implementing the fracture criteria regarding the FFLC and FFLSC. It was concluded that the analytical FFLSC could more realistically predict fracture behaviour better than the FFLC based on strain. In term of percentage error, the analytical FFLSC generated an error less than the FFLC.

On the critical role of martensite hardening behavior in the paradox of local and global ductility in dual-phase steels

The ductility of sheet metal is typically limited by either localized necking or by damage and fracture. A recent ductility classification refers to these failure modes respectively as “global” and “local” formability. The forming limit curve (FLC) and the uniaxial tensile test assess global formability, whereas the fracture forming limit (FFL), the true thickness fracture strain, hole expansion ratios (HER), etc. are indicators of local formability. Experimental hole expansion data in the literature for different dual-phase (DP) steel grades of similar strength and composition presents a paradox: grades which are found to be ductile in a tensile test and/or FLC show a low ductility in hole expansion, whereas other grades with a low ductility in conventional tests perform surprisingly well at cut edges. In this work, an in-depth systematic statistical analysis of idealized artificial two-phase microstructures is carried out to unravel the underlying mechanisms of the observed paradoxical trends. This is done by scaling the hardness of martensite and its volume fraction to generate virtual DP steels of the same strength but different strain hardening and mechanical phase contrast (hardness difference). The proposed micromechanical model adequately reproduces the experimentally observed trends. The results show that in DP steels, a higher global (necking-driven) ductility is obtained upon delaying martensite plasticity by increasing the mechanical contrast of the two phases. Consequently, the stress–strain distributions becomes more heterogeneous, resulting in a lower fracture limit of one of the phases or interfaces in shear loading, thereby, reducing the local ductility. Global ductility is improved by higher mechanical phase contrast and lower martensite volume fraction, whereas local ductility is improved by low phase contrast and higher martensite volume fraction. The hardening behavior of martensite is the key to avoiding the above trade-off between local and global ductility. It is shown that if the strain hardening capacity of martensite in the later stages of deformation (in high strains) can be increased, this would result in removing the observed paradoxical trends of local and global ductility in DP steels.

On the effective peek application for customized cranio-maxillofacial prostheses: An experimental formability analysis

Single Point Incremental Forming (SPIF) is a dieless and flexible forming technology that allows performing complex shapes and presents a high economic payoff for low production series. In this context, this research presents an experimental investigation of Polyether ether ketone (PEEK) sheets deformed by SPIF at room temperature, determining the influence of the process parameters on the material formability. The research is performed in terms of principal strains that are evaluated within the material Forming Limit Diagram (FLD) obtained by means of Nakajima tests allowing to establish the forming limits of PEEK sheet material. On the other hand, the results of the SPIF tests performed gave rise to an analysis in terms of formability, modes of failure, temperature, forming force, and geometry accuracy. These experiments allow assessing the optimal parameters and forming methodologies/procedures for the manufacturing of cranio-maxillofacial prostheses. In this sense, it was performed a global study in terms of the formability of the manufactured prostheses, as well as the shape accuracy, temperature and roughness analysis, among others. This research showed that the maximum strains attainable by the two prostheses were still found far away from the Fracture Forming Limit (FFL) of the material, showing the feasibility to obtain extra formability within the forming safe zone. In conclusion, this work proved the high potential of manufacturing prostheses in the biomedical field using Incremental Sheet Forming (ISF) processes in combination with advanced biocompatible polymers such as PEEK.

Determination of Fracture Limit Line in Principal Strain Space by Shear Tests

The main goal of this paper was to define a new limit line, which expands Forming Limit Curve (FLC) more precisely Fracture Forming Limit Curve (FFLC). The new limit line was defined by damage models transformed from triaxiality-fracture strain space to the major/minor strain space and we focused on the shear area. Because FLC and FFLC have some limitations, for example, some Advanced High Strength Steels (AHSS) fractures before thinning. Another limitation can be seen on the left side of the diagrams in the shear region, where the part can break in the process without crossing the FLC or FFLC. The different shapes of samples were used for finding a new line of the FFLC and Deep Drawing Test (DDT) was used for verification. The fracture points from measurement were used for calibration of simple uncoupled damage models. The simple model means model, which is calibrated based on one or two measurements (tensile test or tensile test + shear test). This paper was used an Advanced High Strength Steel (AHSS) DP1000 sheet with a thickness of 0.8 mm for the experiments.

Development of a ductile failure model sensitive to stress triaxiality and Lode angle

In this paper, an anisotropic failure model proposed by Ganjiani [Ganjiani, M., 2020. A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle. European Journal of Mechanics-A/Solids, 104048] is extended to predict the failure phenomena in the materials. The damage model is sensitive to the stress triaxiality and Lode angle parameters. For considering the anisotropy effects, Hill’s 48 yield function has been used. The model is applied to obtain the failure locus and the corresponding Fracture Forming Limit Diagram (FFLD) to validate the performance of the model. The proposed constitutive equations are implemented into the Abaqus/Standard software via the UMAT code and some numerical examples have been simulated. The simulations mainly focused on the proportionality and non-proportionality effects of loading on the onset of fracture. The predicted results show a good agreement with the experimental data. Comparative investigations between the current model and some failure criteria are also provided. The results indicate the significant potentials of the model to predict ductile failure as well as FFLD especially for anisotropic materials.

Revisiting flangeability in hole-flanging by single-stage incremental forming and conventional process

Recently, hole-flanging by single-stage incremental forming (SPIF) has been proposed as a suitable process to perform hole flanges for small- and medium-sized batches with high flexibility in shape. However, this incremental forming has many differences compared with the conventional press working operation in terms of strain and thickness distributions, failure mechanisms and flangeability measures. In fact, regarding the evaluation of the formability of the flanges, the classical Forming Limit Ratio (LFR) should be used with care to quantify this property in hole-flanging by SPIF. Additionally, the FLC (Forming Limit Curve for necking) and FFL (Fracture Forming Limit) curves, powerful tools for analysing sheet failure in practice, may also yield erroneous prediction of necking in conventional press working or fracture in SPIF. The aim of this work is to present a comparison and analysis of the formability of hole flanges performed by SPIF and press working in AA7075-O sheets. Two complementary parameters to the LFR to compare the flangebility in both operations are discussed, along with the influence of bending induced by the forming tool and the stress triaxiality in the evolution of the principal strains during the forming process. The results point out the limitations in the current practice.

Development of Stress- and Strain-Based Fracture Forming Limit Curves of Sheet Aluminium-Alloy AA2024-T3 through Various Approaches

In this work, four fracture criteria—namely, Fracture Forming Limit Curve (FFLC), Fracture Forming Limit Stress Curve (FFLSC), Fracture Locus (FL) and Fracture Locus Embedded with Bao-Wierzbicki Ductile Damage Criterion (BW-FL)—are comparatively deployed to forecast breakage of deformed AA2024-T3 sheet aluminium-alloy. An FFLC can be experimentally formed by conducting a set of Nakajima stretch-forming based tests. To obtain an FFLSC, such an FFLC drawn in the strain space has to be entirely mapped onto the stress space. This can computationally be accomplished with the help of those well-known plasticity-relevant models like the Hill’48 anisotropic yield criterion and the Swift hardening law. Likewise, both BW-FL and FL in terms of stress triaxialities and critical plastic strains can mathematically be derived from the FFLC incorporated with the Hill’48 anisotropic yield criterion. Hole expansion and tree-point bending tests are carefully carried out both experimentally and simulatively to verify those four generated fracture limits. The more innovative FFLSC and FL demonstrate more accurate prediction on rupture of AA2024-T3 sheet aluminium-alloy than the conventional FFLC. The BW-FL however performs the worst.

A damage model for predicting ductile fracture with considering the dependency on stress triaxiality and Lode angle

This paper aims to present a Continuum Damage Mechanics based fracture model. Two yield surfaces, plastic and damage, are utilized to develop the model. A modified ductile fracture model coupling both stress triaxiality and Lode angle parameter is then proposed. The proposed model is applied to construct the fracture loci of four types of metal alloys: steel HY100, steel PCrNi3MoVA, aluminum 2024-T351, steel TRIP690 and steel A533B. The prediction is also involved investigation of the dependency of damage evolution on stress triaxialities for steel HY100 and steel A533B. The new model is also utilized to construct the Fracture Forming Limit Diagram (FFLD) of steel TRIP690 to validate the performance of the model. The predicted results are in good agreement with the experimental data over a wide range of stress triaxialities. Comparison between the proposed model and some fracture criteria is also provided, and the results indicate that the proposed model has significant potential to predict ductile fracture as well as FFLD at both low and high triaxialities. In order to validate the capability of the model in structural response, the proposed model has been implemented into user-defined subroutines VUMAT in the finite element program ABAQUS/Explicit. For this purpose, the explicit stress integration algorithms of the model have been explained. The model has been validated by comparing the predicted results with experimental data of steel A533B. The results show the excellent correlation between experiments and simulation for the force and damage results as well as the fracture shape.

Investigations on failure-to-fracture mechanism and prediction of forming limit for aluminum alloy incremental forming process

Abstract In order to reveal the evolution mechanism of failure-to-fracture through thickness direction, quantify failure distribution of micro-crack, predict fracture forming limit (FFL) for single point incremental forming (SPIF) with high-speed tool and compare with conventional SPIF, the flow stress model and thermal ductile fracture criterion are calibrated and integrated with the numerical simulation of SPIF process for AA2024-T3 under high-speed tool rotation, and a novel numerical-analytical model is proposed to calculate the damage accumulation. The fracture behaviors appeared in SPIF process in making two typical parts are simulated and verified by experiments. It's found that damage accumulation has stepwise and incremental features, and there is a gradient of damage along thickness direction, which gradually increases so that the fracture through thickness direction can be delayed. The research also revealed that micro-crack will propagate obliquely from the outer surface to certain size along thickness direction almost at the same time at a load path cycle; Afterwards, if the forming tool passes through the failure zone again, the failure will propagate through the whole thickness, finally the fracture appears. Numerical simulation shows that FFL in SPIF with high-speed tool rotation is higher than that in traditional SPIF.

Comparative study of ASS 316L on formability at room temperature and super plastic region

ABSTRACT In the sheet metal industry, hot forming of high strength sheet metal alloys such as austenitic stainless steels (ASSs) are in great demand. Identifying the safe strain region is essential to avoid failures and reduce the wastage. Forming limit diagram (FLD) is a vital tool which is used to describe the maximum limit of principal strains that can be sustained by sheet metals till the onset of localised necking. These diagrams are also useful in comparing the changes in forming characteristics of the material with changes in process parameters like temperature, orientation and speed of deformation. The present study aimed at comparing the experimental FLD for ASS 316L at room temperature and 900°C by stretch forming. These specimens are cut in three different orientations (0°, 45° & 90°) to the rolling direction and experiments are conducted at a strain rate of 0.1/s. It is reported that, the specimens from rolling direction are among the stronger samples. The change in formability characteristics of ASS 316L with changes in temperatures using FLD has been observed. The optical microscopy and scanning electron microscopy is analysed to understand the fracture morphologies. The comparison between these set of results indicates that there is significant increase in formability of material. Abbreviations ASS: Austenitic Stainless Steel; RT: Room Temperature; FLD: Forming Limit Diagram; FFLD: Fracture Forming Limit Diagram; SEM: Scanning Electronic Microscopy; LDH: Limiting Dome Height; UTS: Ultimate Tensile Strength; YTS: Yield Tensile Strength; K: Strength Factor; n: Strain Hardening Exponent

Evaluation of the forming limit of incremental sheet forming based on ductile damage

Abstract Forming limit is a key issue for metallic sheets. As a flexible and dieless manufacturing technology, incremental sheet forming(ISF) process evidently improves the formability of sheet metals. In the present work, based on the assumption of simplified proportional loading in ISF, original formulations of force equilibrium of a micro element under isotropic yield criterion are revisited. Fracture forming limit(FFL) model in contradistinction to the traditional necking one is selected to describe failure mode according to the failure mechanism for AA1050-H111 in ISF. Ductile fracture criterion considering the scope of stress triaxiality is employed for the generalized tensile stress state in ISF process. By combining the equivalent plastic work principle with stress components expressed in the form of process parameters, the proposed modified forming limit model reveals the influence of process parameters, which is in good agreement with experimental results. As for a consistent preoccupation of fracture, the assessment of damage accumulation is presented. Forming height is also evaluated as formability metric in ISF. The modified FFL model is proved to catch practical demand as a guideline of process window design on damage evaluation in ISF.

EVALUACIÓN CRÍTICA DE LA CONFORMABILIDAD EN CHAPA DE AA2024-T3 DEFORMADA MEDIANTE CONFORMADO INCREMENTAL MONO-PUNTO

The evaluation of the enhanced formability in incremental sheet forming processes (ISF), and especially in its simplest variant single point incremental forming (SPIF), has been intensively studied within the sheet metal forming community for the last decade. In general, the formability limit in SPIF is defined by means of the fracture forming limit (FFL). This FFL is usually well above the forming limit curve (FLC), which is the limit controlling failure by necking in conventional sheet metal forming operation on ductile metal sheet. However, low ductility sheet metal such as AA2024-T3 presents usually a fracture-controlled mechanism independent to the forming operation considered. In this context, this paper consist in a critical analysis on formability and failure of AA2024-T3 sheets deformed by SPIF. The study is carried out from a double perspective based on an experimental plan including conventional and incremental forming tests, and numerical simulations using the flow formulation finite element tool DEFORM-3D®. The results show the experimental evidence of a formability enhancement in SPIF above the conventional FFL for this kind of material as well as the necessity of calibrating numerical simulations of these incremental forming processes using experimental data obtained from the corresponding experimental SPIF tests. Keywords: Sheet metal forming, incremental sheet forming (ISF), single point incremental forming (SPIF), formability, fracture.

Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF

Traditionally the fracture in sheet metal forming is characterized by the fracture forming limit (FFL) curve typically obtained by using conventional Nakajima tests. This curve is implicitly assumed a material property. Single point incremental forming (SPIF) is a novel and flexible forming process characterized by the ability to suppress local necking and develop stable plastic deformation up to sheet fracture. In many cases, these fracture strains are clearly above the conventional FFL. The current work presents a numerical study of the evolution of stress triaxiality in SPIF in the ɛ¯−η¯space. The simulations are validated with hole-flanging tests by single-stage SPIF over AA7075-O sheet of 1.6 mm thickness. The difference in the average stress triaxiality at fracture exhibited in SPIF and Nakajima tests would allow explaining the enhancement on formability observed in incremental sheet forming.

On the effect of stress state on the failure limits of hole-flanged parts formed by SPIF

Single Point Incremental Forming (SPIF) is a novel and flexible forming technology that has been used in the last few years to obtain a variety of customized sheet parts. One of the most valuable advantages of this process is its ability to suppress the localized necking of the sheet, allowing a stable plastic deformation up to the ductile fracture of the sheet. Traditionally the fracture in sheet metal forming is characterized by the conventional Fracture Forming Limit (FFL) curve, obtained with Nakazima or Marziniak tests. However, in many cases the SPIF processes exhibit fracture strains clearly above the conventional FFL, showing an unexpected gain of formability. It is well known that ductile fracture in metals is highly affected by the stress state in the material. Therefore, among others, this fact could contribute to explain the experimental differences observed in the FFL obtained by conventional and incremental operations. The present work develops a numerical model in ANSYS to study the mechanics of the fracture process during the incremental deformation operation. The simulations focus on the hole-flanging operation by SPIF in AA7075-O metal sheets of 1.6mm thickness, recently experimentally analysed by the authors. Different configurations of pre-cut hole diameters are simulated. The evolution of the strain paths and the hydrostatic stress in the SPIF process are analysed and discussed. These variables help to explain the apparent enhancement of formability observed in SPIF processes beyond the conventional FFL curve.

Prediction of the formability limit using damage mechanics

Forming limit diagrams (FLD’s) are used to evaluate the workability of metal sheets. These diagrams provide the failure locus at which plastic instability occurs and localized necking develops (commonly designated as the forming limit curve - FLC), and the failure loci at the onset of fracture by tension or by in-plane shear. In this work, the possibility to predict the FLD’s using damage mechanics is presented. Following the approach proposed by Lemaitre [1], the fracture forming limit (FFL) for ductile metals is theoretically derived using the extended Bonora damage model (XBDM). The XBDM is used in numerical simulation with FEM of formability tests (Nakazima and Marciniak) to demonstrate the possibility to account correctly for necking development before fracture. The proposed model prediction was validated with available experimental data for high purity copper.

Prediction of mechanical response for 5000-Series aluminum alloy coupling visco-plastic self-consistent approach with finite element method

In the present work, a hybrid micro macro-approach was adopted to investigate the material behavior of the A5XXX-O object of the Benchmark 3 of Numisheet2018. Starting from the provided uniaxial stress-strain curve and in house microstructure measurements, a mean field approach, by using the VPSC7c code, was used to perform numerical experiments in order to derive the anisotropic macroscopic behavior of the aluminum alloy.Then, at the macroscale, a constitutive model was built on coupling a non-quadratic yield surface function with a damage model developed in the framework of the continuum damage mechanics. Finally, by using MSC.Marc2017.1, finite element simulations of uniaxial and Nakajima bulging tests were performed with the purpose of obtaining the Fracture Forming Limit Curve for the aluminum alloy under investigation.

Sheet Thickness Reduction Influence on Fracture Strain Determination

Standardly, the FLC curve [11] is determined based on ISO12004 according to Nakajima test or Marciniak test [1]. There are two basic influences: the friction between the punch and the specimen and at the same time the pushing the punch on the specimen, which affects the strain distribution over the sheet thickness [17]. The main disadvantage of these tests is the measurement of the linear deformation paths only, but the real forming processes are usually formed in multiple steps processes and the loading path is strongly non-linear. The current trend for sheets formability assessment is investigation of non-linear deformation paths performed on cruciform specimens [2, 3] or using a combination of Marciniak and Nakajima tests [6], [7]. The cruciform specimens should have reduced thickness in the central part in order to assure main plastic deformation and fracture in this region [18]. However, there are indications that the thickness reduction can influence results of the formability assessment. The main goal of this present paper, is experimental investigation of effect of local material thickness reduction on FLC and on Fracture Forming Limit Curve (FFLC). The cruciform specimens with a reduced thickness is investigated with the use of the biaxial stand without friction and pushing the punch. All results are compared to the FLC values.

Characterizing fracture forming limit and shear fracture forming limit for sheet metals

This article investigates, experimentally, the failure loci in transition region between failure by crack-opening by mode I and by mode II of fracture mechanics. This investigation determines the fracture forming limit (FFL) and the shear fracture forming limit (SFFL) for copper with 0.8 mm and brass with 1 mm of thickness, by means of conventional sheet metal tests. Special focus is given to the use of staggered C-slit shear tests in order to obtain fracture strain pairs in the transition zone between FFL and SFFL, and the obtained results are presented. The procedure makes use of circle-grid analysis, thickness measurements and digital image correlation system (DIC). The fracture loci for the copper sheet were validated by simple and complex geometries deformed by single point incremental forming (SPIF). These different geometries allowed to obtain different strain paths (plane strain, shear and bi-axial deformation) with and without fracture, and revealed a good agreement between the results.