Requirements on the yield-to-tensile strength ratio <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, fracture elongation A and the Charpy energy <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> are used together as part of an indirect method of ensuring sufficient ductility at localised areas of stress and strain concentration in the design of steel structures. Recent studies have found that these indirect requirements could be inadequate in certain situations involving cracks or manufacturing defects. Furthermore, requirements on the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> which are enforced regardless of the structural context and other material properties may unnecessarily constrain the use of steels which nonetheless have high strength, fracture toughness and ductility. In contrast to the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, A, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation>, a more direct measurement of a structure’s ability to resist fracture is given by fracture toughness testing, such as J-integral testing, but this is less frequently used, because these tests are significantly costlier than tension and Charpy tests. More often, Charpy tests are performed and correlations between upper-shelf <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> and J values are used to estimate the fracture toughness of the material. However, the existing correlations are predominantly based on empirical findings and have not systematically accounted for the effect of variations in the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, which has been shown in recent studies to affect the fracture toughness. Using a previously validated coupled damage-mechanics model with rate- and temperature-dependent plasticity and damage softening, this paper investigates the correlation between <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation> (the critical J) numerically, including how it is affected by other material certificate properties such as the <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and A. First, a correlation based on regression between the damage parameters and the mechanical properties from mill test certificates is found by calibrating the damage parameters for a large database of these steels. Then, the correlation between <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation> is assessed by simulating the single-edge-notch bending test for a range of varying mill test certificate properties, taking into account how the damage parameters vary with these mechanical properties. The results are analysed to give better insight into how the notch toughness correlates to the fracture toughness, taking the <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and A into account. It is seen that although varying <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and A has some effect on how the total notch energy <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> is correlated to <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation>, it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the <InlineEquation ID="IEq17"> <EquationSource Format="TEX">$C_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation> includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen’s free surface, while <InlineEquation ID="IEq18"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation> primarily concerns the onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$\sigma _y/\sigma _u$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>σ</mi> <mi>u</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and A are seen to have an even smaller effect on the correlation between <InlineEquation ID="IEq20"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation> and the energy (<InlineEquation ID="IEq21"> <EquationSource Format="TEX">$C_{vm}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mrow> <mi mathvariant="italic">vm</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the <InlineEquation ID="IEq22"> <EquationSource Format="TEX">$C_{v}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation>–to–<InlineEquation ID="IEq23"> <EquationSource Format="TEX">$J_Q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>Q</mi> </msub> </math></EquationSource> </InlineEquation> correlation, especially for low <InlineEquation ID="IEq24"> <EquationSource Format="TEX">$C_{vm}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mrow> <mi mathvariant="italic">vm</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>.

Damage-mechanics insights into the relationship between upper-shelf Charpy testing and J-integral testing considering varying tensile test properties

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2026年1月11日

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Wei Jun Wong,
Carey L. Walters

摘要

Requirements on the yield-to-tensile strength ratio $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ , fracture elongation A and the Charpy energy $C_v$ $C_{v}$ are used together as part of an indirect method of ensuring sufficient ductility at localised areas of stress and strain concentration in the design of steel structures. Recent studies have found that these indirect requirements could be inadequate in certain situations involving cracks or manufacturing defects. Furthermore, requirements on the $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ which are enforced regardless of the structural context and other material properties may unnecessarily constrain the use of steels which nonetheless have high strength, fracture toughness and ductility. In contrast to the $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ , A, and $C_v$ $C_{v}$ , a more direct measurement of a structure’s ability to resist fracture is given by fracture toughness testing, such as J-integral testing, but this is less frequently used, because these tests are significantly costlier than tension and Charpy tests. More often, Charpy tests are performed and correlations between upper-shelf $C_v$ $C_{v}$ and J values are used to estimate the fracture toughness of the material. However, the existing correlations are predominantly based on empirical findings and have not systematically accounted for the effect of variations in the $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ , which has been shown in recent studies to affect the fracture toughness. Using a previously validated coupled damage-mechanics model with rate- and temperature-dependent plasticity and damage softening, this paper investigates the correlation between $C_v$ $C_{v}$ and $J_Q$ $J_{Q}$ (the critical J) numerically, including how it is affected by other material certificate properties such as the $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ and A. First, a correlation based on regression between the damage parameters and the mechanical properties from mill test certificates is found by calibrating the damage parameters for a large database of these steels. Then, the correlation between $C_v$ $C_{v}$ and $J_Q$ $J_{Q}$ is assessed by simulating the single-edge-notch bending test for a range of varying mill test certificate properties, taking into account how the damage parameters vary with these mechanical properties. The results are analysed to give better insight into how the notch toughness correlates to the fracture toughness, taking the $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ and A into account. It is seen that although varying $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ and A has some effect on how the total notch energy $C_v$ $C_{v}$ is correlated to $J_Q$ $J_{Q}$ , it does not reflect a significant effect on the ductile fracture initiation toughness but is rather associated with the fact that the $C_v$ $C_{v}$ includes a significant portion of energy for stable ductile propagation and fracture occurring at the specimen’s free surface, while $J_Q$ $J_{Q}$ primarily concerns the onset stage of stable ductile tunnelling behaviour at the centre of the specimen. The $\sigma _y/\sigma _u$ $σ_{y} / σ_{u}$ and A are seen to have an even smaller effect on the correlation between $J_Q$ $J_{Q}$ and the energy ( $C_{vm}$ $C_{vm}$ ) dissipated up to the occurrence of the peak force in the instrumented Charpy test, in comparison with the $C_{v}$ $C_{v}$ –to– $J_Q$ $J_{Q}$ correlation, especially for low $C_{vm}$ $C_{vm}$ .