Loading history dependency of the stress and the displacement for an anisotropic linear elastic material with a crack in frictional contact

摘要

き裂を有する材料に対し，物体境界から圧縮荷重を作用させる場合，物質が弾性体であっても物体内の最終的な応力や変位は，一般に，き裂面に働く摩擦により，物体境界から作用する応力の最終状態によっては一意には決まらず，それらの履歴によって異なる解になる．しかし，圧縮荷重下の応力，変位の荷重履歴依存性を考慮した研究は著者らの知る限りにおいて存在しない．そこで，本論文では，き裂面の滑り，および固着を考慮した境界条件により，いくつかの異なる荷重履歴を与えた場合の，荷重履歴に依存する，極座標表示した具体的な線形異方弾性体の応力，変位の理論解，および応力拡大係数，き裂先端近傍の応力，変位の理論解を求めた．　 In this paper, considering a straight crack in an infinitely extended anisotropic linear elastic material, we obtain a closed form solution of the stress and the displacement. The given far field stresses are such that the crack faces are in frictional contact and may slide against each other. We note that the final stress and displacement in the body do not uniquely determined by the final far field stresses but are dependent on the loading history since the crack faces are in frictional contact. Azhdari, A., et al. obtained the same stress intensity factors as ours for the above mentioned problem without considering the stress boundary conditions. We examine their method in detail in the appendix.