<p>The present contribution aims at the estimation of the formability and failure limit of dual phase (DP600) steel sheets subjected to two-stage forming processes. In this context, in-plane stretch forming experiments were conducted to impart 5% equi-biaxial pre-strain (EBP) to the as-received DP600 sheets. During the second-stage forming, the 5% EBP sheets were subjected to deform using out-of-plane stretch forming and deep drawing test setup. Moreover, three different sample geometries were chosen to impart different stress triaxiality paths during out-of-plane stretch forming tests. The finite element (FE) modeling of the two-stage deformation tests was performed by integrating various anisotropic yield models in the FE simulations, incorporating classical quadratic Hill48-<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16230_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation> and Hill48-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16230_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> models and advanced non-quadratic Barlat Yld2000 model. Additionally, two different ductile damage models, namely the Bao-Wierzbicki (BW) and Lou-Huh (LH) damage models, were included into the FE simulation to estimate the formability of the as-received and pre-deformed materials. It was found that the maximum predicted absolute errors in dome height estimation for as-received DP600 sheets at the onset of fracture were 5.09% and 2.19% during stretch forming and deep drawing tests, respectively, while estimating with the Yld2000 model coupled with LH damage theory in the FE simulation. Furthermore, path-independent polar effective plastic strain (PEPS)–based fracture forming limit diagrams (FFLDs), BW-FFLD, and LH-FFLD were used to predict the fractured dome height for 5% EBP DP600 sheets. It was concluded that the absolute error in fractured dome height prediction was 10.61% and 9.99% while using BW-FFLD, whereas the error value was reduced to 5.92% and 4.67% for LH-FFLD in FE simulation during second-stage stretch forming and deep drawing tests, respectively. Additionally, the fracture initiation point was efficiently predicted using the element erosion method from FE simulation while comparing it with the experimentally deformed domes. The FE predicted stress triaxiality and damage contours showed that the accumulation of damage was quick for EBP sheets. It can be noted that the proposed experimental–numerical path-independent framework is helpful for accurate estimation of the failure before the expensive prototyping or high-volume manufacturing of the autobody parts subjected to the multistage stamping process.</p>

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Numerical and experimental analyses on failure limits of DP600 steel sheets during two-stage forming processes

  • Shamik Basak,
  • Sushanta Kumar Panda

摘要

The present contribution aims at the estimation of the formability and failure limit of dual phase (DP600) steel sheets subjected to two-stage forming processes. In this context, in-plane stretch forming experiments were conducted to impart 5% equi-biaxial pre-strain (EBP) to the as-received DP600 sheets. During the second-stage forming, the 5% EBP sheets were subjected to deform using out-of-plane stretch forming and deep drawing test setup. Moreover, three different sample geometries were chosen to impart different stress triaxiality paths during out-of-plane stretch forming tests. The finite element (FE) modeling of the two-stage deformation tests was performed by integrating various anisotropic yield models in the FE simulations, incorporating classical quadratic Hill48- \(r\) r and Hill48- \(\sigma\) σ models and advanced non-quadratic Barlat Yld2000 model. Additionally, two different ductile damage models, namely the Bao-Wierzbicki (BW) and Lou-Huh (LH) damage models, were included into the FE simulation to estimate the formability of the as-received and pre-deformed materials. It was found that the maximum predicted absolute errors in dome height estimation for as-received DP600 sheets at the onset of fracture were 5.09% and 2.19% during stretch forming and deep drawing tests, respectively, while estimating with the Yld2000 model coupled with LH damage theory in the FE simulation. Furthermore, path-independent polar effective plastic strain (PEPS)–based fracture forming limit diagrams (FFLDs), BW-FFLD, and LH-FFLD were used to predict the fractured dome height for 5% EBP DP600 sheets. It was concluded that the absolute error in fractured dome height prediction was 10.61% and 9.99% while using BW-FFLD, whereas the error value was reduced to 5.92% and 4.67% for LH-FFLD in FE simulation during second-stage stretch forming and deep drawing tests, respectively. Additionally, the fracture initiation point was efficiently predicted using the element erosion method from FE simulation while comparing it with the experimentally deformed domes. The FE predicted stress triaxiality and damage contours showed that the accumulation of damage was quick for EBP sheets. It can be noted that the proposed experimental–numerical path-independent framework is helpful for accurate estimation of the failure before the expensive prototyping or high-volume manufacturing of the autobody parts subjected to the multistage stamping process.