Marciniak Test Research Articles

Formability Characterization Using Curvature and Strain-Rate-Based Limit Strain Detection Methods Applied to Marciniak, Nakazima, and Stretch-Bend Tests

Despite advancements in the characterization of forming limit curves (FLCs) with the development of stereoscopic digital image correlation (DIC), there is still uncertainty in the accuracy of the limit strains, especially in forming operations with out-of-plane bending. The ISO12004-2:2008 standard offers a standardized approach to FLC determination but is not without limitations and is not always applicable to new materials and forming processes (e.g., warm forming, hot stamping). In the present work, a physically based limit strain detection technique is developed, termed the Enhanced Curvature Method (ECM), based on the sheet surface curvature evolution at the onset of necking in sheet formability testing. The ECM is applied to the characterization of 1.1 mm AA5182-O sheet using Marciniak, Nakazima, and stretch–bend characterization tests, and its limit strains are compared with those from the linear best-fit (LBF) local strain-rate approach and the ISO-12004 standard. The ECM considers the physical nature of necking in sheet forming with the aid of thresholds defined in terms of an imperfection metric analogous to the well-known Marciniak–Kuczynski (MK) imperfection factor. By quantifying the evolution of necking, FLCs of different safety margins can be readily generated, enabling a more intuitive selection for the factor of safety. For lower and upper ECM thresholds, the Marciniak plane strain limiting strain was determined to lie between 0.173 and 0.198, respectively, which is comparable to the analytical prediction of 0.194 and in general agreement with the published literature for AA5182-O. Similar plane strain limits were obtained using the ISO and LBF methods with values of 0.188 and 0.208, respectively. The same rankings in limit strain values between methods were observed for plane strain loading in Nakazima and stretch–bend tests.

Evaluating the Plastic Anisotropic Effect on the Forming Limit Curve of 2024-T3 Aluminum Alloy Sheets Using Marciniak Tests and Digital Image Correlation

This study thoroughly investigates the influence of anisotropy on the formability of 2024-T3 aluminum alloy sheets using advanced techniques such as digital image correlation (DIC) and Marciniak tests. A key finding is the relatively small variation in anisotropy values across different strain paths and orientations, contrasting with more significant variations reported in other studies. Tests were conducted on nine samples with various geometries to induce specific strain paths, including uniaxial, plane, and balanced biaxial strains, oriented in different directions relative to the rolling direction. The study also provides a detailed analysis of microstructural and mechanical characteristics, such as precipitate distribution and anisotropy behavior, which are crucial for understanding the relationship between microstructure and material formability. The results show that while anisotropy impacts deformation capacity, the differences in formability among the directions were minimal, with slightly greater formability observed in the diagonal direction. These findings are compared with forming limit curves (FLCs), offering an integrated view of how relatively uniform anisotropic properties influence formability. These insights are essential for optimizing the processing and application of 2024-T3 alloy in industrial contexts, emphasizing the importance of understanding anisotropy in the design of metal components.

A general instability framework for ductile metals in complex stress states from diffuse to acute localization

Adoption of stress-based forming limit curves (FLC) and their equivalent strain representations were introduced to overcome the path dependence of the conventional strain-based FLCs. The stress state and its instantaneous magnitude govern formability such that the triaxial stress state, induced through tool contact, can no longer be neglected. The present work reveals that in addition to the composition of the stress state, the boundary conditions of how the stress is applied to the material determine the onset of plastic instability. To this end, the relatively unknown generalized instability model of Hillier, derived from a stable bifurcation of the stress state under neutral stability, is revisited. Analytical solutions for instability in triaxial plane strain loading were derived for boundary conditions of a proportional, constant, or evolving contact pressure that enables critical evaluation of phenomenological plane stress mapping criteria proposed in the literature. As part of this work, the Hillier instability framework is extended to model the localization process under the constraint of quasi-stable plastic flow in arbitrary principal stress states to form the Generalized Incremental Stability Criterion (GISC). It is shown that the Modified Maximum Force Criterion (MMFC) emerges as one of many special cases of the GISC when restricted to plane stress proportional stressing with a prescribed minor load. Finally, the GISC is applied to Marciniak and Nakazima formability tests of a DP980 steel for identification of appropriate boundary conditions.

Prediction and characterization of forming limits at necking from shear to equi-biaxial loading using the biaxial tensile testing method: Feasibility study and application to AA6061-T4

Determination of forming limit curve (FLC) over a wide range of strain paths can provide a more thorough understanding of sheet metal formability. In this work, for the first time, in-plane biaxial tensile tests employing two distinct cruciform specimens are performed to construct the FLC of AA6061-T4 sheets from shear to equi-biaxial stretching. Four different necking detection methods are investigated in a FE (finite element) procedure to find proper ones for the defined specimens. This procedure consists of the FE modeling of the biaxial tensile test and the Marciniak test. An anisotropic Gurson-Tvergaard-Needleman (GTN) plasticity model based on Hill’48 yield function is calibrated and implemented in simulations to reproduce the anisotropic plasticity and failure behavior of AA6061-T4 sheets. Then, the selected necking detection methods are applied to the biaxial tensile test to experimentally identify the limit strains at necking. The results show that considering two distinct cruciform specimens is an effective solution for the biaxial tensile test to determine the FLC covering a wider range of strain paths. The predicted FLCs show good agreement with the experiments, indicating that the numerical biaxial tensile test combined with the anisotropic GTN plasticity model is an efficient tool for predicting sheet metal formability.

New developments of formability evaluation methods for hot stamping

Formability is an essential material property that needs to be considered when selecting materials for hot stamping applications. Due to the difficulties of achieving rapid cooling before deformation and the failure of lubricant systems, however, it is challenging to use conventional Nakajima and Marciniak tests to evaluate the formability of materials under hot stamping conditions. Recently, biaxial test methods have shown great potential to overcome this challenge. In this paper, recent developments of the biaxial test methods for formability evaluation are reviewed, including testing machines, specimen designs, specimen heating methods, testing procedures, and limit strain determination methods. Compared to the Nakajima or the Marciniak tests, the biaxial test method can provide better simulation for hot stamping conditions and it can be a promising method for evaluating the formability of sheet metals under hot stamping conditions. However, more developments such as the standardisation of the specimen designs and the limit strain determination methods, are still needed for the wide use of the biaxial test method.

Instrumented indentation for determining stress and strain levels of pre-strained DC01 sheets

In classical mechanical testing, determining the stress and strain states of complex shape specimens turns out to be very challenging, especially in the most deformed regions. In the latter case, when not enough material is present, non-destructive testing is needed for determining the corresponding mechanical state. In this study, a novel approach, based on the local quasi-non-destructive instrumented indentation technique (IIT) coupled with the inverse analysis technique (IAT), is used to determine the stress and strain levels of pre-strained DC01 specimens using monotonic and non-monotonic loading paths. Monotonic and cyclic shear tests as well as Marciniak tests, in both plane and equi-biaxial strain states, are used to apply different pre-strain levels. For monotonic loading paths, i.e. monotonic shearing and Marcianiak tests, the applied methodology showed very satisfying results in determining the stress and strain states of the pre-strained specimens, especially for pre-strain values close to the representative indentation strain values. A maximum stress error of less than 15% was obtained in the case of the highest applied pre-strain value (29.04%). The purely isotropic Voce hardening law was adopted for determining the hardening behavior of the studied specimens in both cases: as-received and pre-strained. In the case of cyclic shear, a mixed isotropic-kinematic hardening law is to be used to determine the stress and strain states of the pre-strained specimens. Adopting a mixed isotropic-kinematic Chaboche hardening law led to satisfying results where the estimation errors of the applied pre-strain value and corresponding yield stress didn't exceed 6% and 1.3%, respectively. The obtained results show that the proposed indentation-based method can be very useful in estimating the work-hardening level and corresponding plastic deformation of pre-strained parts under various loading paths

Determination of Forming Limit Curves - Strain Path and Failure Analysis

With the goal to define a cost-effective and efficient process to identify adequate materials for sheet metal forming processes, it is crucial to evaluate the formability of materials. Forming limit curves (FLC) are used to analyze the forming and failure limits of sheet metals and dependence of the major (φ1) and minor strain (φ2) from the uniaxial stress-strain area through the plane-strain point to the biaxial strain area. According to ISO 12004-2, the FLC is performed by Nakajima or Marciniak tests. Due to the experimental setup and the preconditions, pre-stretching occurs in the specimens and bending and friction effect are the result. The determination of the onset of necking (FLC) results mathematically from a “best-fit inverse parabola” on section lines. In addition, the failure point, i.e. the maximum strain value one frame before failure, is also analyzed. In contrast, tensile, notched tensile and hydraulic bulge tests, which together have a potential to map an alternative FLC, exhibits a linear strain path evolution. The behavior of the various strain paths of Nakajima and the alternative methods are examined for necking and cracking. Furthermore, the fracture surfaces are investigated by confocal laser scanning microscopy to identify influences of the different FLC methods on the fracture mechanics. FLCs were conducted with the Nakajima and the alternative FLC characterization method for a ductile steel (DX54D). To ensure transferability, the tensile tests are also performed with a high-strength steel (DP800). The FLC of the ductile steel, generated through the alternative method, exhibits a similar shape to the Nakajima generated FLC with the advantage of a constant strain rate leading to linear strain paths and a lower number of tests. The same results are achieved for the uniaxial strain tests with DP800.

Influence of the Anisotropic Behavior on Equibiaxial Paths

Marciniak and Nakajima tests are commonly used in building FLD's, since they allow covering all regions from uniaxial to almost equibiaxial strain paths. In this work, the deviation from equibiaxial strain paths is analyzed as function of the material anisotropic behavior. The numerical results show that material with present equibiaxial stress and strain paths, while for the ones with the paths are neither equibiaxial in stress nor strain. Moreover, it is shown that despite the similarities between the two tests, they present different sensitivity to the control of the blank holder force and to the friction coefficient. Namely, the stress and strain paths in the Marciniak specimen center are more sensitive to the control of the blank holder force. On the other hand, the stress and strain paths in the Nakajima specimen center are more sensitive to the friction coefficient. The deviation from the equibiaxial strain path indicates that the stress ratio is also not necessarily 1.0, meaning that the stress triaxiality and the Lode parameter also present some deviation from the reference values for an equibiaxial stress state. This should be taken into account when analyzing forming limit results.

Predicting ductile fracture during biaxial sheet stretching using an ellipsoidal void model

Ductile fracture during biaxial sheet stretching for two types of ferrous alloys and one type of nonferrous pure metal was predicted using the ellipsoidal void model proposed by one of the authors. First, fracture forming limit obtained experimentally by the Nakajima test scarcely differed from that obtained experimentally by the Marciniak test. Next, fracture forming limit obtained by the experiment scarcely depended on the magnitude of prestrain, which was applied to the sheet by rolling, and scarcely depended on the type of prestrain. Since the number of material constants on ductile fracture is only one, the material constant was determined so that the material thickness at fracture calculated from the simulation agreed with that obtained by the experiment. Fracture forming limit calculated using the ellipsoidal void model agreed closely with that obtained by the experiment, whereas fracture forming limit calculated using conventional ductile fracture criteria differed from that obtained by the experiment. Furthermore, fracture forming limit calculated using the ellipsoidal void model and that calculated using the conventional ductile fracture criteria changed drastically when the strain ratio changed across one for simulating biaxial stretching using a prestrained sheet.

Microstructure, Anisotropy and Formability Evolution of an Annealed AISI 430 Stainless Steel Sheet

The effect of the microstructure on the principal strain paths (uniaxial, plane, and biaxial) in the formability processes of ferritic stainless steel AISI 430 sheets is studied. The Marciniak test (determination of the plastic strain of sheet metal with a flat tip punch) is applied to determine the forming limit curves and different strain levels in the strain paths by the digital image correlation technique. The formability is discussed in light of the microstructure, standard mechanical properties, work hardening behavior, and anisotropy measurements (R‐value). Electron backscatter diffraction analysis is carried out to determine the texture of the selected strain paths. The texture evolution shows a marked γ (<111>// normal direction [ND]) fiber and cube ({001} <100>) texture component under the biaxial strain mode, whereas the α (<110>// rolling direction [RD]) fiber is somewhat favored under uniaxial plane strain. The results are compared with texture simulations performed under the fully constrained Taylor model, finding reasonable agreement with the experimentally measured main components.

Characterization of the Formability of High-Purity Polycrystalline Niobium Sheets for Superconducting Radiofrequency Applications

Abstract The forming limit diagram (FLD) of high-purity niobium sheets used for the manufacturing of superconducting radiofrequency (SRF) cavities is presented. The Marciniak (in-plane) test was used with niobium blanks with a thickness of 1 mm and blank carriers of annealed oxygen-free electronic (OFE) copper. A high formability was measured, with an approximate true major strain at necking for plane strain of 0.44. The high formability of high-purity niobium is likely caused by its high strain rate sensitivity of 0.112. Plastic strain anisotropies (r-values) of 1.66, 1.00, and 2.30 were measured in the 0 deg, 45 deg, and 90 deg directions. However, stress–strain curves at a nominal strain rate of ∼10−3 s−1 showed similar mechanical properties in the three directions. Theoretical calculations of the forming limit curves (FLCs) were conducted using an analytical two-zone model. The obtained results indicate that the anisotropy and strain rate sensitivity of niobium affect its formability. The model was used to investigate the influence of strain rate on strains at necking. The obtained results suggest that the use of high-speed sheet forming should further increase the formability of niobium.

Comparative Investigation of the Experimental Determination of AA5086 FLCs under Different Necking Criteria.

The construction of a forming limit diagram (FLD) is a conventional approach to obtain limit strains and to evaluate the formability of sheet metal. Appropriate necking criteria should be applied to determine the forming limit curve (FLC) accurately. In recent years, deep research on the determination of the FLC has been carried out; meanwhile, several necking criteria have been proposed. However, the application of inappropriate necking criteria would cause deviations when determining FLCs. In this study, both Marciniak and Nakajima tests were carried out on the AA5086 aluminum sheet to make a comparative investigation of different necking criteria in the determination of FLCs. In the Marciniak test, four existing necking criteria were chosen to construct FLCs, and analyzed in detail. The well-performed time dependent and position dependent methods were selected for the Nakajima test. Meanwhile, the modified Wang method based on the height change of the adjacent points was proposed. The comparative results showed that the time and position dependent methods were relatively conservative in both experiments, while the modified Wang method could identify the onset of localized necking more accurately.

Constitutive, Formability, and Fracture Characterization of 3rd Gen AHSS with an Ultimate Tensile Strength of 1180 MPa

<div class="section abstract"><div class="htmlview paragraph">The superior formability and local ductility of the emerging class of third generation of advanced high-strength steels (3rd Gen AHSS) compared to their conventional counterparts of the same strength level offer significant advantages for automotive lightweighting and enhanced crash performance. Nevertheless, studies on the material behavior of 3rd Gen AHSS have been limited and there is some uncertainty surrounding the applicability of developed methodologies for conventional dual-phase (DP) steels to this new class of AHSS. The present paper provides a comprehensive study on the quasi-static and dynamic constitutive behavior, formability characterization and prediction, and the fracture behavior of two commercial 3rd Gen AHSS with an ultimate strength of 1180 MPa that will be contrasted with a conventional DP1180. The hardening response to large strain levels was determined experimentally using tensile and shear tests and then validated with 3-D simulations of tensile tests. In general, the strain rate sensitivity of the two 3rd Gen AHSS was significantly different as one grade exhibited larger transformation-induced behavior. The in-plane formability of the three 1180 MPa steels determined using Marciniak tests was similar but with a stark contrast in the local formability for the 3rd Gen AHSS. The forming limit curves could be accurately predicted using the experimentally measured hardening behaviour and the modified Bressan-Williams through-thickness shear model. An efficient experimental approach to fracture characterization for AHSS was developed that exploits tool contact and bending to obtain fracture strains on the surface of the specimen by suppressing necking. Miniature conical hole expansion and biaxial punch tests are used along with the VDA 238-100 bend test.</div></div>

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

Evolution of a forming limit curve for non-linear strain paths induced on advanced high-strength sheet steel with its proven applicability to a complex deep-drawing process

In this work, nonlinear forming limit curves were developed through a systematic combination of both experimental and numerical tools. FLCs derived from both intact and pre-stretched DP440 high-strength steel (HSS) sheet were involved. First of all, prepared sheet specimens were, in compliance with the Marciniak test procedure, in-plane pre-stretched in either of the following three directions, uniaxial tension, plane strain and biaxial, at varying strain levels. Afterwards, each distinguishingly pre-strained specimen was post-strained until fracture following the Nakajima test guideline. The so-called displacement function could be determined out of these experimental data. An individual nonlinear IFU-FLCs was approximated with the help of the base linear FLC, the formulated displacement function and a unique simulated strain path collectively gathered from the local fracture zone. Two yield models, Hill’48 and Yld2000- 2d, were tried during strain-path calculations to observe how different yield models would alter the paths and thus developed nonlinear FLCs. From the study, notable variation was detected. In the end, validity of such nonlinear FLCs were proven through a complex-shaped industrial stamping part. The IFU-FLC noticeably-better defined forming limits of parts experiencing nonlinear strain paths than the conventional one.

On the experimental characterization of sheet metal formability and the consistent calibration of the MK model for biaxial stretching in plane stress

Analytical formability models based upon in-plane proportional plane stress loading such as the Marciniak–Kuczynski (MK) model are commonly evaluated against forming limit curves (FLCs) obtained using Nakazima tests with out-of-plane deformation, non-linear strain paths and tool contact. The present study has conducted a comprehensive experimental characterization of a DP1180 advanced high strength steel with relatively low formability to demonstrate that the use of Nakazima FLC data can lead to a physically inconsistent MK model. Although good agreement can be obtained using the MK model with Nakazima data, it is attributed to calibration bias in the hardening model and selection of the imperfection factor. Marciniak tests should be performed to characterize the FLC or process-corrections be applied to the Nakazima FLC to then calibrate the MK imperfection factor. An analysis of the MK framework reveals a false dependence of the imperfection factor on the hardening model due to artefacts in the hardening model calibration. When the Considère constraint for the uniform elongation is imposed during the hardening model calibration, the MK imperfection factor becomes nearly independent of the choice of hardening model. The accuracy of the FLC predicted by the MK model, when appropriately constrained and calibrated in a deterministic manner, was in a reasonable agreement with the experimental data only after accounting for material anisotropy. In contrast, the deterministic Modified Maximum Force Criterion (MMFC) model provided a very close estimate of the experimental forming limit strains of the mildly anisotropic DP1180 using both isotropic and anisotropic yield functions.

Experimental Characterization and Deterministic Prediction of In-Plane Formability of 3rd Generation Advanced High Strength Steels

The objective of the current study is to develop a practical, deterministic approach to the prediction of the in-plane formability of two third generation advanced high-strength steels (AHSS) of 980 and 1180 MPa ultimate tensile strength using only quasi-static mechanical property data. The hardening response to large strains was experimentally measured with the use of simple shear and tensile tests and validated in tensile simulations. The process-corrected limit strains in the Nakazima and Marciniak tests were compared to various analytical Forming Limit Curve (FLC) models for in-plane stretching. It was observed that the widely-used Marciniak–Kuczynski model can adequately predict the experimental FLC in biaxial stretching but significantly underestimated the limit strains in uniaxial stretching for both third generation AHSS. The observed through-thickness shear fracture mode in biaxial stretching was reasonably well-captured by the Bressan–Williams (BW) instability model for the 1180 MPa steel. A proposed extension of the BW model to uniaxial tension by adoption of the maximum in-plane shear stress criterion (BWx model) provided superior experimental correlation relative to the zero-extension model of Hill that was too conservative. Finally, a linearized version of the modified maximum force criterion (MMFC) was proposed that markedly improved the correlation with the process-corrected FLC for in-plane stretching of AHSS. The developed framework for FLC prediction was then applied to a DP980 AHSS and an AA5182 aluminum alloy from the literature. The DP980 corroborated the observed trend for the two third generation AHSS whereas the MK and the BWx models performed best for the AA5182 with its saturation-type hardening behavior and non-quadratic yield surface.

Accounting for the effect of heterogeneous plastic deformation on the formability of aluminium and steel sheets

Forming limit curves characterise “mean” failure strains of sheet metals. Safety levels from the curves define the deterministic upper limit of the processing and part design window, which can be small for high strength, low formability materials. Effects of heterogeneity of plastic deformation, widely accepted to occur on the microscale, are neglected. Marciniak tests were carried out on aluminium alloys (AA6111-T4, NG5754-O), dual-phase steel (DP600) and mild steel (MS3). Digital image correlation was used to measure the effect of heterogeneity on failure. Heterogeneity, based on strain variance, was modelled with the 2-component Gaussian mixture model, and a framework was proposed to (1) identify the onset of necking and to (2) re-define formability as a probability to failure. The results were “forming maps” in major-minor strain space of contours of constant probability (from probability, P = 0 to P = 1), which showed how failure risk increased with major strain. The contour bands indicated the unique degree of heterogeneity in each material. NG5754-O had the greatest width (0.07 strain) in plane strain and MS3 the lowest (0.03 strain). This novel characterisation will allow engineers to balance a desired forming window for a component design with the risk to failure of the material.

Analysis of forming limit behaviour of high strength steels under non-linear strain paths using a micromechanics damage modelling

The formability characteristics of advanced high strength (AHS) steel grades 780 and 1000 subjected to varying forming histories including strain path changes were described by means of a damage modelling approach. The Marciniak tests of the examined steels were firstly carried out to apply pre-strains under various deformation modes. Afterwards, tensile, stretch-bending and hole expansion test of the pre-strained samples were performed. FE simulations coupled with the Gurson-Tvergaard-Needleman (GTN) ductile damage model were conducted to predict failure occurrences of AHS samples in the two-stage forming tests. The damage model parameters were determined under consideration of pre-strain effects on void evolution mechanisms and its interdependencies with microstructure constituents of steels, for which hybrid methods of metallographic analyses, local strain measurement and representative volume element (RVE) simulations were employed. Then, forming limits of the investigated steels in different forming procedures with non-proportional loading paths were characterized. It was shown that the micromechanics damage simulations in combination with the proposed parameter identification scheme could precisely represent the fracture states of steels under such complex forming conditions.