Fracture Forming Limit Diagram Research Articles

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.

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].

Exploring deformation mechanics of temperature assisted incremental forming with hybrid heating

The single point incremental forming (SPIF) process is a die-less rapid prototyping sheet metal forming method, extensively researched for over two decades. SPIF shows higher formability compared to conventional sheet forming methods. Deformation of materials such as magnesium (Mg) is favored at elevated temperatures due to their poor room temperature formability. Past studies have explored heat-assisted forming techniques to achieve improved formability in SPIF. However, the underlying mechanics of deformation is sparsely explored. The present work explores the mechanism of formability improvement based on thermal gradients for SPIF in hybrid heating. The SPIF experiments are conducted for a combination of local and global heating conditions achieved using tool contact friction and cartridge heaters. The local temperature, stress distributions, and limiting strains are obtained numerically. Fracture-forming limit diagrams (FFL) are developed, and numerical predictions are validated using experimental strain measurements under different forming conditions.

Predicting ductile fracture during extended Miyauchi shear testing using analytical model

In the fracture forming limit diagram, it is known that the major strain at fracture increases with increasing the minor strain at fracture in sheet shear testing. In this study, ductile fracture during an extended Miyauchi shear testing was predicted using an analytical model. First, an extended Miyauchi shear testing was proposed, in which the angle between the line segment that connects two neighboring notch roots and the tensile direction of the specimen was set to be an arbitrary value between zero and π/2. Next, an analytical model for the extended Miyauchi shear testing was proposed, in which the deformation of the sheet before localized necking and that after localized necking were analyzed in the region surrounding the line segment connecting two neighboring notch roots, and ductile fracture was predicted. Finally, the major strain at fracture and the minor strain at fracture obtained by the experiment for nine angles between zero and π/2 were compared with those calculated using the analytical model and those calculated using the ellipsoidal void model proposed previously by the author. Special attention was paid to the effect of prestrain which was imparted to the sheet by rolling on ductile fracture. When the angle is equal to zero, the major strain at fracture and the minor strain at fracture obtained by the experiment, agreed with those calculated using the analytical model, and did not agree with those calculated using the ellipsoidal void model.

Use of uncoupled ductile damage models for fracture forming limit prediction during two-stage forming of aluminum sheet material

In this paper, failure limits of aluminum AA5052 sheet material were experimentally investigated, and subsequently, these were predicted using various uncoupled ductile fracture models. In this context, three different sets of experiments, namely two-stage stretch forming, two-stage deep drawing, and single point incremental forming experiments, were performed to estimate the failure limits under several different strain paths. Both the isotropic von Mises and anisotropic Barlat Yld2000 yield criteria were used to calibrate eight different fracture models, and found that incorporating an anisotropic model enhanced the accuracy of prediction for most of the fracture models. Moreover, it was identified that the incorporation of anisotropic yield theory in the Bao-Wierzbicki (BW) fracture model predicted the experimental fracture surface strains precisely for as-received sheet materials. This BW model-based fracture forming limit diagram (BW-FFLD) was transposed into a path-independent polar effective plastic strain (PEPS) locus to estimate the onset of fracture during two-stage forming experiments. Furthermore, the BW model was incorporated as a fracture initiation model in the finite element (FE) software, LS-Dyna, using the generalized incremental stress state dependent damage model (GISSMO) platform to predict the fracture location and dome height through the element erosion technique. It was observed that the dome height and cup height were predicted within 7 % and 5 % error margins in the FE simulation of two-stage stretch forming and deep drawing experiments, respectively. Furthermore, the damage evolution contour indicated that the accumulation of the damage value was rapid, which was responsible for the massive drop in the dome and cup heights during two-stage stretch forming and deep drawing experiments.

Deep drawability of additively manufactured sheets with a structured core

The deep drawability of additively manufactured stainless steel sheets with a core structure is investigated. By fracture forming limit diagrams it is shown that the additively manufactured sheets reveal good formability. The deep drawing process is analyzed numerically and the numerical models are validated experimentally. The main failure mode is a fracture of the face sheets. No severe deformation of the core structure was encountered, leading to the fact that the parts keep their structural integrity after the deep drawing process. It is shown that the process forces can reasonably be predicted by a modified Siebel’s method. A process window diagram is derived, e.g. showing a maximum deep drawing ratio βmax = 1.4 for honeycomb structures with a relative core density of ρcore = 0.22.

Modeling anisotropic ductile fracture of AA7075-T6 sheet for sheet metal forming considering anisotropic stress state

Anisotropic ductile fracture is one of the critical issues in the precision plastic forming of lightweight sheet metals. In this work, a new anisotropic ductile fracture model is developed by introducing the anisotropic stress triaxiality into the weight equation of the shear-controlled ductile fracture criterion. In an attempt to consider the effect of material anisotropy on stress state, the proposed fracture model is constructed in the anisotropic stress state form. The proposed anisotropic fracture model is used to characterize the anisotropic ductile fracture behavior of the AA7075-T6 sheet with a thickness of 2.0 mm under various stress states at room temperature. A series of uniaxial tensile tests are conducted using the in-plane shear specimen, the specimen with a central hole, and the plane strain grooved specimen to experimentally investigate the ductile fracture of AA7075-T6 along rolling, diagonal, and transverse directions. The proposed fracture model is calibrated by fracture strains determined from the hybrid experimental–numerical approach. With the calibrated fracture model, the anisotropic ductile fracture behaviors of AA7075-T6 over a wide range of stress states are predicted and compared with experimental measurements. The results show that the proposed fracture model successfully captures the anisotropic ductile fracture behavior of AA7075-T6 under various stress states at room temperature. Furthermore, to further illustrate the fracture predictive capability of the proposed fracture model, the predicted anisotropic fracture forming limit diagram is compared with the experimental forming limit strains obtained from the literature. Reasonable agreement is shown between literature data points and predicted fracture forming limit diagram. Accordingly, the proposed model has a great advantage in quantitative characterizing the anisotropic ductile fracture of high-strength aluminum alloy sheets under various loading conditions.

Experimental and numerical investigation of forming limit diagram of Al/Cu two-layer sheet in high strain rate forming process

The formability of a two-layer sheet in the electromagnetic forming (EMF) process is investigated through experimental and numerical methods. The Al/Cu two-layer sheet is fabricated by using an explosive joint in the EMF process. By using the diameter changes in surface grids of specimens with various widths the forming limit diagrams used in necking and fracture conditions are calculated. The acceleration of the major strain method is used to predict the necking time in the simulation. The J-C damage constants were calibrated by using the surface response method with a 95% model fit. The Al/Cu two-layer sheet has a higher formability in the EMF process than in a static condition. The Al/Cu two-layer sheet’s formability increases when the Cu is in the outer layer. The Cu layer has a higher formability than the Al layer and has a protective role against necking. The fracture forming limit diagram is linear and has a negative slope. The fracture strain in the in-plane strain condition in the AC lay-up is 36% greater than the CA lay-up, due to Cu’s better resistance to fracture in tensile stress.

Effect of natural aging time on anisotropic plasticity and fracture limit of Al7075 alloy

Numerical approaches for fracture modeling have been proposed for various metallic materials, including high-strength steels and aluminum alloys. However, the quantitative relationship between the Portevin–Le Chatelier (PLC) effect and the fracture initiation has not been yet fully explored, considering the influence of the natural aging time (NA) on the material deformation behavior. To address this gap, this study investigated the PLC effect on the anisotropic plasticity and fracture limit of Al7075 alloy according to the natural aging time. Aging behavior and PLC effects are experimentally evaluated through uniaxial tensile and fracture tests using the 3D digital image correlation method. The natural aging-dependent PLC effect is tracked in the visualization of the strain rate map and thickness strain distributions with plastic deformation. Variations in the anisotropic plasticity are captured using Barlat’s YLD2000‐2d anisotropic yield function at different natural aging times, and fracture envelopes that cover general 3D stress states are identified based on the Lou–Huh ductile fracture criterion. A natural aging-dependent fracture modeling approach is proposed to predict the influence of natural aging on the fracture limit transition. Finally, the strain- and stress-based fracture forming limit diagrams, including their corresponding magnitude of the stress vector, are represented. The results reveal that no general trend for the natural aging-dependent fracture limit based on the strain metric is observed, whereas the fracture limit based on the stress metric tends to increase with natural aging in various loading conditions.

Effect of Formability Process Parameters in Dynamic Strain Ageing Region of Austenitic Stainless Steel

The consumption of Austenitic Stainless-Steel ASS 304 has been increasing recently in the outer body of Automobileapplications. Sheet Metal Forming is one of the processes used to convert ASS 304 sheet into an end product. ASS 304 hasgood ductility with the rise in temperature up to 450oC and later dynamic strain aging (DSA) in the temperature range 450-600oC. Formability studies of ASS 304 in the DSA region and the effect of process parameters like anisotropy and strainrate are investigated in the present paper. Stretch forming Investigations have been carried out at a temperature of 500oC intwo quasi-static strain rate ranges 1x 10-4 s-1 and 1x 10-1 s-1 concerning three orientations parallel (R0), diagonal (R45) andTransverse(R90) to Rolling Direction. The experiments were carried out at both the necking and fracture regions. Deformedspecimens' major and minor strains are measured to plot Fracture Forming limit Diagrams, strain distribution, and limitingDome height. Particular attention is given to the evaluation of strain rate and orientation of the sheet concerning rollingdirection on formability.

Prediction of fracture limits of IN625 alloy by coupling ductile damage models and anisotropic yielding functions with the classical Marciniak and Kuczyński model

The fracture forming limit diagram (FFLD) is gaining special attention in high strength materials where the necking tendency rarely occurs during sheet metal forming processes. In the present work, the classical Marciniak and Kuczyński (MK) model has been modified by coupling it with different ductile damage models (Cockcroft and Latham, Brozzo, Oyane, Ko, Oh, Rice and Tracey, McClintock and Clift) and anisotropic yielding functions (Hill 1948 and Barlat 1989) to predict the fracture limits of Inconel 625 (IN625) alloy at different temperatures. Firstly, uniaxial tensile testing has been conducted for the determination of important mechanical properties. Consequently, stretch forming experiments have been performed to analyze the forming limits of a material. It has been found that the safe and fracture forming limits of the material increased by approximately 17.26% and 22.22%, respectively, on increasing the temperature from 300 to 673 K. From the comparative analysis of different combinations of ductile damage models and yielding functions, the Cockcroft and Latham (C-L) damage model in combination with the Barlat 1989 yielding function helped in best predicting the theoretical FFLD as it displayed the least average root mean square error (RMSE) of 0.033. The other ductile damage models used for predicting the theoretical fracture limits displayed large error; hence, they should not be considered while designing a critical component in the manufacturing industry using IN625 alloy.

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.

Prediction of fracture limits of Ni–Cr based alloy under warm forming condition using ductile damage models and numerical method

The stretch forming and the deep-drawing processes were carried out at 300 and 673 K to determine the safe forming and fracture limits of IN625 alloy. The experimentally obtained strain-based fracture forming limit diagram (FFLD) was transformed into a stress-based (σ-FFLD) and effective plastic strain (EPS) vs triaxiality (η) plot to remove the excess dependency of fracture limits over the strains. For the prediction of fracture limits, seven different damage models were calibrated. The Oh model displayed the best ability to predict the fracture locus with the least absolute error. Though the experimentally obtained fracture limits have only been used for the numerical analysis, none of the considered damage models predicted the fracture strains over the entire considered range of stress triaxiality (0.33<η<0.66). The deep drawing process window helped to determine wrinkling, safe and fracture zones while drawing the cylindrical cups under different temperature and lubricating conditions. Further, the highest drawing ratio of 2 was achieved at 673 K under the lubricating condition. All the numerically predicted results of both stretch forming and deep drawing processes using the Hill 1948 anisotropic yielding function were found to be good within the acceptable range of error.

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.

Determining Forming Limit Diagrams Using Sub-Sized Specimen Geometry and Comparing FLD Evaluation Methods

Sheet metal forming boundaries are established using the forming limit diagram (FLD). The Nakajima and Marciniak tests, which are based on stretching a material using a punch, are the most commonly used methods for determining the FLD or fracture forming limit diagram (FFLD). The results are usually evaluated by calculating local strain, strain rates, specimen thickness reduction or fracture strain. When the amount of experimental material is insufficient, miniaturization of the testing specimens may be a solution. However, the interchangeability of the results for standard and miniaturized specimens has not been proven yet. In this study, the Nakajima tests were performed using standard and sub-sized specimens made of manganese–boron steel 22MnB5, commonly used in the automotive industry. Afterwards, four FLD/FFLD evaluation methods were applied and compared. The miniaturized specimens yielded higher strain values, which was explained by the varied ratio of material thickness/punch diameter and different bending conditions. The highest compliance of the results was recorded for the standard and miniaturized FFLD.

Relationship between mechanical properties in 42SiCr and 42SiMn medium-carbon steels and austempering temperatures

Sheet metal forming boundaries are established using the forming limit diagram (FLD). The Nakajima and Marciniak tests, which are based on stretching a material using a punch, are the most commonly used methods for determining the FLD or fracture forming limit diagram (FFLD). The results are usually evaluated by calculating local strain, strain rates, specimen thickness reduction or fracture strain. When the amount of experimental material is insufficient, miniaturization of the testing specimens may be a solution. However, the interchangeability of the results for standard and miniaturized specimens has not been proven yet. In this study, the Nakajima tests were performed using standard and sub-sized specimens made of manganese–boron steel 22MnB5, commonly used in the automotive industry. Afterwards, four FLD/FFLD evaluation methods were applied and compared. The miniaturized specimens yielded higher strain values, which was explained by the varied ratio of material thickness/punch diameter and different bending conditions. The highest compliance of the results was recorded for the standard and miniaturized FFLD

An improved M–K model coupled with different ductile criteria for fracture limit predictions of Inconel 718 alloy

Fracture Forming Limit Diagram (FFLD) is gaining special attention for high strength materials like Inconel 718 alloy where the substantial necking tendency rarely seen. The present study mainly aims at accurate evolution of forming limits for Inconel 718 alloy with an improved Marciniak–Kuczynski (M–K) model coupled and various ductile fracture criteria. Firstly, uniaxial test has been performed for analyzing material properties and anisotropic parameters. The stretch forming tests have been conducted to evaluate the limiting forming limits of Inconel 718 alloy. Subsequently, an improved M–K model coupled with ductile fracture criteria has been developed for the theoretical prediction of the fracture strains. The different ductile fracture criteria, namely; Clift, Cockcroft and Latham, Oyane and Brozzo, have been implemented in the improved M–K model. A Newton–Raphson method has been used to solve improved M–K model. The improved M–K model coupled with Oyane's fracture criterion has shown good predictability of the fracture loci with the least average absolute errors and root-mean-square deviation (Δavg = 0.075 and RMSD = 0.105).

Effect of pre-cut hole diameter on deformation mechanics in multi-stage incremental hole flanging of deep drawing quality steel

Incremental hole flanging (IHF) is a relatively new sheet metal forming process to produce intricate shapes without using dedicated punches and dies. The present work focuses on understanding the mechanics of the multi-stage IHF process through experimental studies and the finite element approach. The IHF experiments were performed on deep drawing quality steel sheets with a pre-cut hole diameter of 45 mm, 50 mm, 60 mm, and 70 mm. The cylindrical flanges were formed in four stages with an initial wall angle of 60° to a final angle 90° with an angle increment of 10° in each stage. The maximum and minimum hole expansion ratio was found to be 2.06 and 1.17 respectively. The fracture was observed in a blank of 45 mm pre-cut hole diameter in the third stage at 40 mm depth. The fracture forming limit diagram (FFLD) was determined from incrementally formed varying wall angle conical and pyramidal frustums. Consequently, six different ductile damage models incorporating Hill48 anisotropy plastic theory were successfully calibrated. The Ayyada model showed good agreement with experimental FFLD as compared to all other models. The fracture limit determined experimentally and using the Ayyada model was implemented in the finite element simulation of the IHF process to predict the formability in terms of in-plane strain distribution, forming forces, and thickness distribution. The predicted results matched accurately with the experimental data within a 6% error for all investigated conditions. Noticeably, the strain path in IHF had three deformation modes viz. plane strain, bi-axial stretching, and uni-axial tension, which was comprehended using texture analyses. Finally, irrespective of the initial pre-cut hole diameter, the surface roughness was found to decrease with the number of stages of the IHF process.

An effective method for determining necking and fracture strains of sheet metals

Biaxial tensile testing methods using cruciform specimens have been developed in the last few decades for the determination of forming limit diagrams (FLDs) and fracture forming limit diagrams (FFLDs) for sheet metals. One of the difficulties associated with this test geometry is the lack of a widely accepted method to determine the necking and fracture strains which are necessary to construct these diagrams. In this study, a novel spatio-temporal method has been proposed for the determination of necking and fracture strains. In the method, two rectangular zones: the base zone (BZ) and the reference zone (RZ) are selected at the location where fracture initiates. The zone RZ includes the zone BZ and both zones have the same side length in the direction parallel to the necking band but different side length in the perpendicular direction. By plotting the thickness reduction within RZ against that in BZ, the onset of localised necking can be determined by finding the intersection of the two straight lines fitted separately using the data in the initial and final stages of deformation. The corresponding limit strains are then determined using the strains within the zone BZ. The method has been successfully applied to uniaxial tensile tests on AA6082 and boron steel dog-bone specimens, and to equi-biaxial tensile tests on AA5754 cruciform specimens.• Compared to widely used existing methods, the novel spatio-temporal method has greater simplicity, stability and accuracy with regard to the determination of localised necking strains.• The spatio-temporal method has good potential to become a standard method for the determination of limit strains for sheet metals.

Effect of non-associated flow rule on fracture prediction of metal sheets using a novel anisotropic ductile fracture criterion

The ductile fracture behavior of anisotropic materials was investigated and modeled by the uncoupled ductile fracture criterion for aluminum alloys 6016-AC200. The ductile fracture model takes into account micro-mechanisms of void nucleation, void growth, and evolution of void coalescence. The anisotropic yield function and non-associated flow rule were applied to increase the accuracy of the ductile fracture prediction. Series of uniaxial tensile tests, equi-biaxial tension test, and hydraulic bulge test were utilized to identify coefficients of the plasticity model. Various standard fracture tests covering a wide range of stress triaxiality from negative to moderate and high-stress triaxiality were used in order to calibrate the ductile fracture parameters for AA6016-AC200. The strain field on the surface of specimens was captured by the non-contact measurement DIC system for all tests. The fracture surface, fracture locus, and fracture forming limit diagram constructed by the proposed ductile fracture criterion were plotted. These basic fracture tests and a square cup drawing test were simulated by the ABAQUS/Explicit commercial software to verify the efficiency of the proposed fracture criterion and the advanced plastic model in predicting the onset of ductile fracture behavior. The results indicated that the proposed ductile fracture criterion can be utilized for predicting the onset of the anisotropic ductile fracture behavior in sheet metal forming.