Biaxial Loading Effect on Higher-Order Crack Tip Parameters

Abstract

The higher-order asymptotic crack-tip fields are considered for a Mode I in power-law plastic and creeping materials under plane strain conditions. Using an asymptotic expansion and separation of variables for the stress function, a series solution is obtained for stress components at a crack tip. In addition, full-field finite element analysis based on a modified layer approach is employed to model the effects of biaxial loading on nonlinear behavior. Loadings were applied related to a range of biaxial stress ratio (−2, +2). The radial and angular stress distributions and higher-order amplitude coefficients for plastic materials are obtained. Crack tip higher-order fields under various conditions of biaxial loading and spanning the range of times from small scale creep to extensive creep are presented. Account is taken of the radial distance accompanying crack tip blunting. The phenomenon of stress redistributions along crack plane on creep time as a function of biaxial stress ratio is stated. The regions of dominance of the HRR-type field under various biaxial stress ratio, crack distance, hardening exponent, and creep time are found. Good agreement analytical findings with finite element results conforms that HRR-solution corresponds only to the equi-biaxial tension which is a particular case of biaxial loading. It is further demonstrated that the higher-order both for plastic and creeping fields are controlled through constraint parameter A2 by biaxial stress ratio. By fitting numerical results for plastic and creeping materials, two empirical formulas were obtained to describe the higher-order terms amplitude coefficients A2 distributions depending on biaxial stress ratio, crack distance, hardening exponent, and creep time.

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

“…To cover both region distances, values and are chosen for creeping material. More details concerning the determination of both A 1 and A 2 amplitude factors are presented by the authors 5,26 . presented dependencies (Fig.…”

“…More details concerning the determination of both A 1 and A 2 amplitude factors are presented by the authors. 5,26 presented dependencies ( Fig. 7) correspond to full range of the normalized creep time from the smallscale creep conditions (characterized byt = 0.0925) to extensive creep conditions (t = 46.25) when the crack-tip distance r is scaled by C/(σ 0ε0 ).…”

Characterizations of material constraint effect for creep crack in center weldment under biaxial loading

“…O'Dowd et al (1999) also performed a study on the biaxial effect on the center cracked plate. According to Shlyannikov et al (2009), the crack tip field was controlled by biaxial ratio through higher order constraint parameters regardless of creep or elastoplastic solids.…”

Поле Напряжений У Вершины Трещины При Смешанном Нагружении В Условиях Плоского Напряженного Состояния

“…Смешанное нагружение трещины (нормальный отрыв и поперечный сдвиг) в условиях плоского напряженного состояния. Вопросы смешанного нагружения элементов конструкций с трещинами и угловыми вырезами являются предметом пристального исследования научного сообщества в самое последнее время [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. В [6] разработан метод и приведены результаты вычислений упругопластических коэффициентов интенсивности напряжений в полном диапазоне смешанных форм деформирования от нормального отрыва до чистого сдвига.…”

“…sin 2θ r α σ (5) . Структура поля скоростей деформаций для M p = 0.75 совпадает с совокупностью формул (11), но углы, соответствующие линиям раздела секторов, имеют другие числовые значения, указанные в формулах (10).…”