木材の破壊条件に関する理論的考察

Abstract

通常, 切欠きをもつ木質部材の破壊予測には線形破壊力学を用い, 切欠きをもたない部材についてはvon Misesなどの破壊条件を用いて解析を行なっている。本研究では線形破壊力学の概念を包含し, かつ, 切欠きをもつ部材ももたない部材も同ーの解法で解けるような両者の統一的な解法として"有限小領域理論"を提案した。すなわち, "切欠き付近についても弾性論的に応力解析を行ない, 有限小領域の平均応力が破壊条件に達した時破壊が生じる"とする考え方である。本研究では試行錯誤の結果, 有限小領域として繊維方向1mm, 繊維に直角方向0. 4mmの長方形領域を用いた (2次元平面応力問題)。解析例として中央に長方形の切欠きをもつ梁の曲げ試験を取り上げ, 小試験体および実大梁の実験結果と, FEMを用いて解いた有限小領域理論によるクラック進展予測荷重を比較した。その結果, 両者によい一致の得られることを確めた。また同時に, 比較のため線形破壊力学すなわち応力拡大係数Kおよびひずみエネルギ解放率gによる予測も行ない, 有限小領域理論の有効性を確めた。

To estimate the fracture load of wooden structural elements with notches LEFM (linear elastic fracture mechanics) is unsually used. And to estimate those without notches, von Mises's criterion or such is used. Considering the basic concept of LEFM, "Finite Small Area Theory" was proposed in this study as the unified theory for the above two cases i. e. with and without notches. The essence of proposed thery is that fracture occurs when average stresses at finite small area satisfy the criterion of von Mises i. e. eq. (17). For the finite small area aL×σR.T, 1mm (in grain direction)× 0.4mm (perpendicular to the grain) was used in this study through trial and error. For the application example, analyses of bending test problems of wood beams with rectangular notches were carried out. And good agreement was observed between the theoretical results and the experimental results, which were obtained with small specimens and also normal sized timber beams. Analyses by means of LEFM i. e. stress intensity factor K and energy release rate g were also carried out for the comparison to the finite small area theory, and the validity of the proposed theory was observed.