Fracture Forming Limit Curve Research Articles

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.

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.

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.

Characterizing the fracture forming limit curve from shear to uniaxial tension in ultrathin sheet metals using specimens with cutouts

Characterizing the fracture forming limit curve from shear to uniaxial tension in ultrathin sheet metals using specimens with cutouts

An Improved Approach for Forming Limit Prediction of Strongly Anisotropic Thin-Walled Tube Combining M–K Model and Ductile Fracture Criterion

Abstract Accurate prediction of the forming limit at necking of strongly anisotropic thin-walled tubes is an urgent requirement in tube hydroforming. M–K model is one of the most widely used prediction models. However, the failure criterion in M–K model is based on the ratio of major true strain increments in the groove to uniform regions, which sometimes results in overestimation of the limit strains. To address this issue, a combined model of M–K model and ductile fracture criterion (DFC) for tube was proposed in this paper, in which the failure condition of the groove region is determined by the DFC. The characteristics of the M–K + DFC model were analyzed by combining with the DF2012 phenomenological DFC. To validate the M–K + DF2012 model, the limit strains at necking of an AA6061 tube with strong in-plane anisotropy were tested through tube-controllable biaxial loading experiments. The results show that the forming limit curve (FLC) predicted by the M–K + DFC model does not exceed the FLC calculated by the M–K model and the fracture forming limit curve (FFLC) determined by the corresponding DFC. The M–K + DF2012 model provides a reasonable forming limit prediction of the AA6061 tube, and the shortcoming of the M–K model mentioned earlier is overcome. Meanwhile, a reasonable constitutive model considering the in-plane anisotropy is very important in the forming limit prediction of a strongly anisotropic thin-walled tube.

Fracture Analysis of Sheet Aluminum Alloy AA2024-T3 Through a Complex-Loading Cross-Die Test

Lightweight materials such as aluminum alloys are, nowadays, well recognized as one of the most popular choices in the aerospace industry owing to their fantastic strength-to-weight ratio. Their fabricability is, nevertheless, doubtful down to their low elongation, especially in the present day where geometrical complexity is hugely demanded. Truly understanding fracture behaviors of such sheet metal would benefit all involved parties. To achieve that challenging goal, proper fracture-analysis models and implementation methods are definitely crucial. This work proposes the recent Lou–Huh fracture criterion to describe the rupture behavior of sheet aluminum alloy AA2024-T3. To build such a damage mechanics model, a string of Nakajima stretching and notched tensile tests must be performed to acquire critical strain data, precisely measured using the 2D-DIC principle. The data are used to calibrate the model. A fracture locus (FL), defining an extensive AA2024-T3 fracture threshold, is then established out of the fine-tuned model. The FL is directly coupled into an ABAQUS/Explicit FE process simulation model via the Fortran-based subroutine VUMAT. This leading-edge implementation can supposedly emulate realistic damage evolution by monitoring and actively removing the elements whose degree of injury has reached a certain limit. At the end, the complete integrative FE model is empirically validated through an industrial X-shaped specimen, deformed under nonlinear strain paths. Fracture locations, shapes and development on the FE-simulated specimen are observed and contrasted with those on the experimental one. It is obviously shown that the results from both approaches agree remarkably well in all aspects. When compared with the famous fracture forming limit curve (FFLC), the Lou–Huh FL combined with the element-removal VUMAT implementation clearly outperforms. In summary, the proposed model and the implementation procedure are practically outstanding fracture evaluators of AA2024-T3, wonderfully predicting and vividly laying bare crack appearance and growth.

Comparison of two CDM-based models for necking and fracture limits of metal sheets under hot stamping conditions

A unified viscoplastic constitutive model based on continuum damage mechanics (CDM) has been recently developed for the prediction of forming limit curves (FLCs) and fracture forming limit curves (FFLCs). In this CDM model, two damage variables which are strain path dependent (so called strain-based model) have been introduced to model the necking and fracture limits in sheet metal forming. In this study, the two damage variables have been modified by replacing the strain components with stress components to model stress path dependence (so called stress-based model). Then the two sets of CDM models have been analysed and compared in respect to their computational accuracy and efficiency. For this purpose, all the material constants in the models have been calibrated using the recently published data of 22MnB5 boron steel sheet under hot stamping conditions. Subsequently, the two models together with the calibrated material constants have been implemented into the commercial software ABAQUS using a user subroutine VUMAT, and applied to biaxial tests for the computation of both the necking and the fracture limit strains at hot stamping temperatures. Computational results show that there is little difference between the two CDM models with respect to the computed limit strain values, but the strain-based CDM model is more time-efficient.

A CDM-based unified viscoplastic constitutive model of FLCs and FFLCs for boron steel under hot stamping conditions

Forming limit curves (FLCs), which are constructed using the limit strains at localised necking, are the most widely used tools for the evaluation of the formability of sheet metals. Fracture forming limit curves (FFLCs) are more recently developed, complementary tools for formability evaluation which are instead constructed using the limit strains at fracture. Since the formability depends strongly on forming conditions such as strain state, temperature and strain rate, models for predicting FLCs and FFLCs are essential for the optimisation and further application of hot forming processes in which these forming conditions vary significantly with both position and time. However, no model has so far been developed to predict FFLCs either alone or in conjunction with FLCs for sheet metals such as boron steel under hot stamping conditions. In this study, a set of unified viscoplastic constitutive equations for the prediction of both FLCs and FFLCs based on continuum damage mechanics (CDM) has been formulated from a set of recently developed constitutive equations for dislocation-based hardening, in combination with two novel coupled variables characterising the accumulated damage leading to localised necking and fracture. The novel variables take into account the effects of strain state, temperature and strain rate on the formability of sheet metals. The material constants in the CDM-based constitutive equations have been calibrated using experimental data comprising true stress-true strain curves and limit strains of a 22MnB5 boron steel obtained at a range of temperatures and strain rates. Investigation of the effect of varying selected parameters in the coupled damage variables on the resulting computed FLCs and FFLCs has demonstrated the flexibility of the model in enabling curves of different shapes and numerical values to be constructed. This indicates the potential of the CDM-based constitutive model for application to other materials for warm or hot stamping processes.

Experimental studies of necking and fracture limits of boron steel sheet under hot stamping conditions

Boron steel is the most widely used material in hot stamping applications for forming automotive body panels with complex shapes and ultra-high strength. Due to the high austenitic transformation temperatures and the complex thermal cycle required for hot stamping, however, it is difficult to evaluate the formability of the material using standard punch test methods developed for room-temperature testing. In this study, a high-temperature modification of a recently developed biaxial test method has been used to determine, in a single test procedure and for the first time, forming limit curves (FLCs) and fracture forming limit curves (FFLCs) for 22MnB5 boron steel sheet with a thickness of 1.5 mm under thermal conditions that are representative of industrial hot stamping processes. A direct resistance heating strategy has been developed, and a recently proposed cruciform specimen design has been modified for high-temperature use. For tests with target temperatures in the range of 750 to 925 °C, the resulting test specimens had the highest temperature at the specimen centre and a temperature difference of less than 45 °C in the gauge area and fracture occurred close to the centre of this area under all test conditions investigated. Limit strains at the onset of necking and at fracture for the material have been determined by applying digital image correlation (DIC) to obtain full-field strain measurements, providing an experimental foundation for constructing both FLCs and FFLCs for industrial applications.

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.

Biaxial test method for determination of FLCs and FFLCs for sheet metals: validation against standard Nakajima method

Recently, a biaxial test method comprising a cruciform specimen design and spatio-temporal method to determine the limit strains has been proposed for the determination of forming limit curves (FLCs) and fracture forming limit curves (FFLCs) for sheet metals. However, this test method has not yet been validated against the existing standard methods. In the present work, this biaxial test method has been applied to the aluminium alloy AA5754 for formability evaluation at room temperature and results from the biaxial test method have been compared with those from the standard Nakajima method. Theoretical analysis has been carried out to compare equi-biaxial tension cases for the two methods; a similar variation of thickness strain with radial distance normalised by the radius of the gauge area is found between the two methods. In the biaxial tests, decreasing the radius of the through-thickness dome profile, with which the gauge area is thinned, leads to fracture nearer the specimen centre but produces a less uniform strain distribution. Importantly, the major strains at necking on the FLC, as determined using the biaxial and the standard test methods, are almost the same in the plane-strain state, while in other strain states, the major strains are slightly lower for the biaxial method than that for the Nakajima method. An FFLC for AA5754 has also been determined using the biaxial test method, in which the major strain at fracture decreases with increasing strain ratio β from −0.5 to 0, while it changes only slightly when β > 0.

Anisotropic fracture forming limit curve and its applications for sheet metal forming with complex strain paths of aluminum sheet

Anisotropic fracture forming limit curve and its applications for sheet metal forming with complex strain paths of aluminum sheet

Incremental sheet forming of steel/polymer/steel sandwich composites

Abstract Formable three- or multi-layer metal/polymer/metal sandwich sheets are interesting functional materials replacing pure metallic sheets in various applications due to the arbitrary tailoring of their mechanical properties and thicknesses delivering the application-related properties. Forming of such sandwiches is often more limited compared to mono-metallic sheets due to the load conveying mechanism through their thin skin sheets. To extend and improve the forming potential of the sandwich sheets, single point incremental forming (SPIF) was used for the first tests shaping conical profiles with variable and constant wall angles in addition to semi-spherical ones. The forming limits were identified in terms of the limiting wall angle, part height and the surface strains determined by digital image correlation. The results reveal that shaping of the sandwich composites sheets is possible and similar to monolithic metal sheets, but with earlier failing of more than 30%. Failure of the sandwich sheets by cracking and delamination as well as galling is expected. Additionally, the sine law used normally to describe the thickness at failure of SPIF was applied and verified. Besides, the fracture forming limit curve could be used to describe their forming limits. Applying two-stage SPIF could extend the forming potential compared to the single-stage SPIF of the same part angle.

Modeling anisotropic ductile fracture behavior of Ti-6Al-4V titanium alloy for sheet forming applications at room temperature

An anisotropic modified Mohr–Coulomb (MMC) ductile fracture criterion was developed to characterize the ductile fracture behavior of the Ti-6Al-4V titanium alloy at room temperature. The stress triaxiality is inherently coupled within the ductile fracture criterion and shows an exponential effect on the material ductility decay. The effect of the Lode angle is considered as well, considering a parabolic trend. The fracture criterion was developed based on the direction-independent plastic strain-rate increment called isotropic equivalent plastic strain-rate increment. To incorporate the influence of directionality on the ductile fracture behavior, the fourth order linear transformation tensor was successfully introduced. The Ti-6Al-4V fracture behavior under uniaxial tension, in-plane shear, plane strain along various loading orientations, and equi-biaxial tension states of stress was successfully predicted using the newly developed fracture criterion. Furthermore, the theoretical Fracture Forming Limit Curve (FFLC) predicted by the anisotropic ductile fracture criterion was compared with experimental forming limit curves from literature. The results show that the developed phenomenological anisotropic MMC ductile fracture criterion has a great advantage to predict the ductile failure of sheet metals characterized by strong anisotropy.

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 theoretical prediction framework for the construction of a fracture forming limit curve accounting for fracture pattern transition

It has been accepted that the formability of a sheet metal with a moderate ductility can be limited by not only localized necking (LN), but also ductile fracture (DF). In this study, a theoretical prediction framework is developed for a comprehensive formability characterization, in which forming limit curves at LN (FLCN) and DF (FLCF) are elaborately correlated by considering strain path evolution. A dual-phase steel material (DP590 sheet metal) is selected with a series of DF and Nakajima tests performed. A newly proposed DF model (uncoupled type) is calibrated by implementing a hybrid experiment-simulation method in line with the DF tests, which are designed to achieve DF under distinct stress states, such as simple shear (SS), uniaxial tension (UT), plane strain tension (PST), and balanced biaxial tension (BBT). The resulting three dimensional (3D) fracture surface demonstrates a good agreement with the tested data. The modified maximum force criterion (MMFC) is selected for the theoretical identification of strain path evolution. The calibrated MMFC results in a FLCN exhibiting a certain level of underestimation as compared to the tested data in the range of positive minor strain. The MMFC is improved (iMMFC) by incorporating with an initial strain path-based function for a higher accuracy in characterizing evolutive strain paths; the resulting FLCN is observed to have a better performance than that of MMFC. Theoretical FLCFs are determined by the integral of ductile damage increment (defined by the DF model calibrated) over each identified strain path from UT to BBT. After considering strain path evolution, different deformation stages are added into the finalized forming limit diagrams including both FLCF and FLCN. It is found that the FLCF based on iMMFC model demonstrates acceptable deviations as compared to all the tested cracking data. Moreover, this FLCF intersects with the corresponding theoretical FLCN as load path approaches from UT to BBT, representing a fracture pattern transition from a LN band-accompanied DF to the one without LN band; this prediction is further validated by experimental observations. The FLCF based on MMFC fails to predict this transition behavior. The current study confirms the presence of a competition between LN-induced failure and DF-induced failure for sheet metals. Moreover, all of these findings advance the insight into the importance of performing a DF prediction aside of a FLCN prediction, especially for the case where a sheet metal with a moderate ductility shows a fracture pattern transition behavior.

Formability and forming force in incremental sheet forming of AA7075-T6 at different temperatures

The AA7075-T6 sheet recently received attention, owing to its low weight and strength for use fabricating automotive parts (e.g., body, motor case). Owing to its low ductility and high strength at room temperature, it is difficult to form; a heating process is required. In this paper we investigate the mechanical properties of a 1.0-mm-thick AA7075-T6 sheet at different temperatures via an uniaxial tensile test, examining the forming characteristics of incremental sheet forming (ISF) at different temperatures. In the ISF experiment, a sheet clamped on a fixed die was heated and maintained at the designed temperature. The forming force was measured by an in situ force monitoring system. The forming parameters included tool diameter, vertical step, temperature, and feed speed. Vertical step and temperature were selected at three levels for experimental design. The formability was evaluated by varying the shapes of wall-angle conical frustums. When the temperature increased to 200 °C, the formability increased dramatically. The fracture-forming limit curve in ISF was defined for this material at different temperatures. This fracture criterion was loaded into ABAQUS software to predict fracture. The comparison between experimental and finite-element method simulation shows good agreement.

Experimental determination and numerical prediction of necking and fracture forming limit curves of laminated Al/Cu sheets using a damage plasticity model

Different mechanical, physical and chemical properties such as high strength-low weight structures, good corrosion resistance and appropriate thermal and electrical conductivity of multi-layer sheet metals have increased their applications in industry and research community. In this study, the forming behavior of a two-layer metal sheet during the hemispherical punch stretching test is investigated. The laminated sheet is fabricated from the AA1050 aluminum and 1100 copper sheets using the explosive welding. Various geometries of the laminated sheet for two different lay-ups are utilized to induce different stress states during the hemispherical punch stretching test. By measuring the strain pairs of the fractured specimens, the necking forming limit curve (NFLC) and the fracture forming limit curve (FFLC) of the two-layer sheet are experimentally achieved. In order to numerically predict limiting strains at the necking and fracture initiation, a time-dependent method and the modified Xue–Wierzbicki damage plasticity model incorporating effects of the hydrostatic pressure and the Lode angle parameter are respectively employed in the Abaqus/Explicit finite element (FE) code using the user subroutine VUMAT. It is shown that using a hybrid numerical-experimental approach, both the NFLC and FFLC of the Al/Cu two-layer sheet can be well predicted. Using the damage model, the participation of effective factors at the onset of fracture is described and it is experimentally shown that cracks begin to initiate and propagate from the outer layer. Results also show that the Al/Cu two-layer sheet would have a higher fracture and necking limiting strains when the punch comes into contact with the inner aluminum layer.

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.

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.