本研究主旨在探討受內壓容器或構件的J 值估算方法，以具表面
裂縫受雙軸拉力平板為研究模型，評估以參考應力解為基礎的J 值估
算模式的適用性。比較並找出適當的參考應力解，配合有系統的三維
有限元素分析的驗證，重新修正參考應力解以符合有限元素分析結
果。並探討參考應力法估計J 值時的適用範圍及各參數(如受力比λ、
裂縫深度比a/t、裂縫形狀參數a/c、裂縫前緣位置對應的角度φ等)對
其估計準確性的影響。
研究結果顯示不同的雙軸受力比(λ)會影響參考應力解與有限元
素分析解的符合程度，需修正參考應力解。本研究提出對λ=0.5及1.0
之雙軸向受力修正因數η ，經修正後二者得到良好的一致性。另由
有限元素分析結果發現，隨著負荷比增加，不同裂縫幾何參數組合下
的J/Je值逐漸離散，裂縫形狀參數a/c值是造成離散的原因，而負荷比
與材料硬化指數(n)的增加，擴大了離散的幅度。整體而言於負荷比
≦1.25 時與有限元素分析值最大差異量不超過20%。
對表面裂縫而言，裂縫前緣各位置之J值均不相同，參考應力法
對近表面點與裂縫前緣各位置的J值估算亦能與有限元素分析結果吻
合，但對於表面點(φ=0o)位置，鑑於表面點力場的複雜性，參考應力
法並不適用於表面點J值的估算。
經研究結果證實參考應力法可應用於不同應變硬化指數的材
料，參考應力法將J 值估算過程簡化成數個方程式，不需使用曲線轉
化及查表內插等易產生誤差的運算，是可廣泛使用且簡便的J 值估算
工具。

In this study, different J-estimation methods for a surface-cracked plate under
biaxial tension compared and the applicability of the reference stress approach is also
evaluated. Systematic 3-D finite element analyses (FEAs) are performed for
determining the best reference stress solution and providing the guidance for
modification of the reference stress approach. The limit of the application for the
reference stress approach was investigated and the effects of the parameters such as
biaxial ratio (λ), relative crack depth (a/t), aspect ratio (a/c), and the angle related to
the position along the semi-elliptical crack front (φ) are discussed.
Results showed that the biaxial ratio has certain effects on the agreement
between the reference stress approach predictions and FEA results. After being
modified by a modification factor η, the reference stress approach showed much
better estimates of the J value. The FEA results indicated that the estimated value of
J/Je scattered as the load ratio increased. The scattering was attributed to the effects
of aspect ratio (a/c) and enlarged with increasing load ratio and strain-hardening
exponent. However, for all cases considered, the differences between the reference
stress approach and FEA in J-estimation are less than 20% for load ratios below 1.25.
For surface-cracked component, the non-linear J distribution along the crack
front may be different. The proposed reference stress approach in this study
provided good estimations of the J-integral not only at the near surface point but also
at an arbitrary point along the crack front. Due to the complication of crack tip
stress field at the surface point (φ = 0), the J-estimation approach proposed here was
considered as unsuitable for the surface point.
Results showed the proposed reference stress approach of J-estimation were
also applicable to the cracked components with different strain hardening exponent
values. The reference stress approach provided the J estimates in closed-form
equations without using the curve-fitting process or interpolation. Apparently, such
an approach provides a simplified and comprehensive engineering tool for
J-estimation.

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