<p>This study investigated the traction–separation law (TSL) of glass fiber-reinforced polymer composite laminates considering the fiber-bridging effect under mixed-mode I/II loading conditions. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode bending (MMB) tests were conducted to analyze the fracture behavior under mode I, mode II, and mixed-mode I/II loading conditions. Finite-element analysis (FEA) was performed by applying various TSLs, that is, a trilinear TSL considering fiber bridging for mode I loading conditions and a bilinear TSL without considering fiber bridging for mode II loading conditions along with the B–K fracture criterion. To estimate the bridging strength (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\sigma }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>σ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation>), a key parameter in TSL under mode I loading conditions, traction–separation test results were utilized instead of conventional DCB test results. Moreover, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation>, used to construct TSL under mixed-mode I/II loading conditions, was defined as a function of the bridging strength from the TSL under mode I loading conditions, fiber orientation (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>), and mode mixture (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">${G}_{\text{II}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>II</mtext> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq5"> <EquationSource Format="TEX">${G}_{\text{T}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>T</mtext> </msub> </math></EquationSource> </InlineEquation>). Assuming that <InlineEquation ID="IEq6"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> could not exceed the bridging strength, four cases were analyzed: (1) <InlineEquation ID="IEq7"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> = 0, (2) <InlineEquation ID="IEq8"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> = <InlineEquation ID="IEq9"> <EquationSource Format="TEX">${\sigma }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>σ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation>, (3) <InlineEquation ID="IEq10"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> as a function of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>, and (4) <InlineEquation ID="IEq12"> <EquationSource Format="TEX">${\tau }^{b}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>τ</mi> </mrow> <mi>b</mi> </msup> </math></EquationSource> </InlineEquation> as a function of both <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq14"> <EquationSource Format="TEX">${G}_{\text{II}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>II</mtext> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq15"> <EquationSource Format="TEX">${G}_{\text{T}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>T</mtext> </msub> </math></EquationSource> </InlineEquation>. A comparison of the load–displacement curves obtained from the FEA and MMB tests revealed that the results based on the function considering both <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq17"> <EquationSource Format="TEX">${G}_{\text{II}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>II</mtext> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq18"> <EquationSource Format="TEX">${G}_{\text{T}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>T</mtext> </msub> </math></EquationSource> </InlineEquation> exhibited the highest agreement with the experimental data in all cases.</p>

Traction–Separation Law of Multidirectional GFRP Composite Laminates Considering Fiber Bridging Effect Under Mixed-Mode I/II Loading Conditions

期刊论文
发表日期：

2025年7月2日

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Hyun-Jun Cho,
In-Gul Kim

摘要

This study investigated the traction–separation law (TSL) of glass fiber-reinforced polymer composite laminates considering the fiber-bridging effect under mixed-mode I/II loading conditions. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode bending (MMB) tests were conducted to analyze the fracture behavior under mode I, mode II, and mixed-mode I/II loading conditions. Finite-element analysis (FEA) was performed by applying various TSLs, that is, a trilinear TSL considering fiber bridging for mode I loading conditions and a bilinear TSL without considering fiber bridging for mode II loading conditions along with the B–K fracture criterion. To estimate the bridging strength ( ${\sigma }^{b}$ $σ^{b}$ ), a key parameter in TSL under mode I loading conditions, traction–separation test results were utilized instead of conventional DCB test results. Moreover, ${\tau }^{b}$ $τ^{b}$ , used to construct TSL under mixed-mode I/II loading conditions, was defined as a function of the bridging strength from the TSL under mode I loading conditions, fiber orientation ( $\theta $ $θ$ ), and mode mixture ( ${G}_{\text{II}}$ $G_{II}$ / ${G}_{\text{T}}$ $G_{T}$ ). Assuming that ${\tau }^{b}$ $τ^{b}$ could not exceed the bridging strength, four cases were analyzed: (1) ${\tau }^{b}$ $τ^{b}$ = 0, (2) ${\tau }^{b}$ $τ^{b}$ = ${\sigma }^{b}$ $σ^{b}$ , (3) ${\tau }^{b}$ $τ^{b}$ as a function of $\theta $ $θ$ , and (4) ${\tau }^{b}$ $τ^{b}$ as a function of both $\theta $ $θ$ and ${G}_{\text{II}}$ $G_{II}$ / ${G}_{\text{T}}$ $G_{T}$ . A comparison of the load–displacement curves obtained from the FEA and MMB tests revealed that the results based on the function considering both $\theta $ $θ$ and ${G}_{\text{II}}$ $G_{II}$ / ${G}_{\text{T}}$ $G_{T}$ exhibited the highest agreement with the experimental data in all cases.