Theoretical fracture mode model for torsion test of spot welds

Abstract Resistance spot welds subjected to torsion testing according to ISO 17653 exhibit two predominant fracture modes, namely interfacial fracture and button-pulled fracture. Their occurrence is governed by the interplay of weld diameter, sheet thickness, local microstructural condition, and, in conventional welds, the effective sheet thickness reduction caused by electrode indentation. In this study, a theoretical fracture mode model is developed that combines these geometrical and mechanical influences and describes the fracture transition as a finite transition zone rather than as a single critical weld diameter. The model is based on theoretical considerations of the torsional section modulus and incorporates a reduction factor $$\chi _{\textrm{BH}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> </mml:math> to account for locally different heat-treatment states in the weld region. Its predictive capability is validated experimentally using two investigation series with different steel sheet combinations. In series S1 , a four-sheet configuration is used to eliminate the influence of electrode indentation, whereas series S2 represents conventional two-sheet spot welds in which indentation effects are present. For the statistical evaluation, the reduction factor is varied. The results show that the predictive performance exhibits a distinct optimum and that the fracture transition is best represented by a parameter-dependent interval of the reduction factor in the range $$\chi _{\textrm{BH}}=0.7 \dots 0.85$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.7</mml:mn> <mml:mo>⋯</mml:mo> <mml:mn>0.85</mml:mn> </mml:mrow> </mml:math> . For series S1 , the highest mean agreement between predicted and observed fracture modes is obtained at $$\chi _{\textrm{BH}}=0.75$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.75</mml:mn> </mml:mrow> </mml:math> with 97.3%. For series S2 , the highest mean agreement without considering electrode indentation is 86.2% at $$\chi _{\textrm{BH}}=0.70$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.70</mml:mn> </mml:mrow> </mml:math> , whereas inclusion of $$e_{\textrm{max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>e</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:math> increases the mean agreement to 92.2% at $$\chi _{\textrm{BH}}=0.75$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.75</mml:mn> </mml:mrow> </mml:math> . These findings confirm that reliable prediction requires both a micro-structure-related correction by $$\chi _{\textrm{BH}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mtext>BH</mml:mtext> </mml:msub> </mml:math> and the consideration of indentation-induced geometric effects. The proposed model provides a physically interpretable and statistically substantiated basis for fracture mode prediction in torsion-tested spot welds. In addition, the study highlights the value of torsion testing as a destructive reference method for the validation of modern imaging non-destructive testing approaches, particularly ultrasonic methods that provide spatially resolved information in the joining plane.