The strength of polycrystalline metals increases with a decrease in grain size according to the HallPetch relationship. However, heterogeneous microstructures deviate from this relationship depending on the distribution of grain sizes. This paper introduces a rule of mixtures based approach for determining the characteristic length of the microstructure for heterogeneous weld metal. The proposed grain size parameter, the volume-weighted average grain size, is measured experimentally for nine structural steel weld metals and two base materials. The weld metals are found to have a large variety of grain size distributions that are noticeably broader than those of the base material due to differences in phase contents. The results show that the volume-weighted average grain size is able to capture the influence of grain size distribution on the strength of welded structural steel. Based on the experimental results, a modified Hall-Petch relationship is formulated for the strength prediction of heterogeneous microstructures. The modified relationship is also found to be applicable to data from the literature.

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A B S T R A C T The paper investigates the influence of highly localised stress distribution around the notch tips of the laser stake-welded T-joints to the slope of the fatigue resistance curve. The study considers experimental data of eight series involving joints under tension or bending loads. Various boundary conditions and plate thicknesses are considered. The stress distribution in the singularity-dominated zone ahead of the notch tips is investigated by means of the finite element analysis. The aim is to relatively distinguish the stress distribution from one case to another. The growth rate of the elastic singular stress with respect to the distance from the tip is described by the dimensionless gradient. This gradient is equal to the slope of the linear stress-distance function when presented in double-logarithmic scale. The slope of the fatigue resistance curve varies approximately from 4 to 8. It is observed that the change of the slope can be closely associated with the gradient of the maximum principal stress evaluated in the plane that is orthogonal to the crack path. The orthogonal plane corresponds to the maximum principal stress direction. In contrast, there is a large scatter in the relation between the slope and the gradient evaluated in the commonly assumed crack plane. The study shows that the dimensionless gradient exhibits sensitivity towards plate thicknesses, local weld geometry and the loading condition.Keywords laser stake-welds; fatigue testing; J-integral; stress gradient; stress state. N O M E N C L A T U R Ea 1 , a 2 = notch depths [mm] C = material constant [À] e weld = offset of weld [mm] E = Young's modulus [MPa] h g = distance between joint plates [mm] J =J-integral [MPa mm] k ϕ = rotational stiffness [kN] l p = length of panel [mm] m = slope of the fatigue resistance curve [À] n = exponent of a stress function [À] N f = number of cycles to failure [À] s = spacing of web plates [mm] t f = face plate thickness [mm] t w = web plate thickness [mm] t weld = thickness of weld [mm] u i = node translation [mm]; i = x, y, z ΔF = force range [kN] ΔJ =J-integral range [MPa mm] ΔK I = range of stress intensity factor for fracture mode I [MPa mm 0.5 ] ΔK II = range of stress intensity factor for fracture mode II [MPa mm 0.5 ] θ MAX = direction of the maximum principal stress [°] θ MTS = initial crack propagation angle [°]

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