Exact solutions of near crack line fields for mode I crack under plane stress condition in an elastic-perfectly plastic solid

Abstract

The near crack line analysis method has been used in the present paper. The classical small scale yielding conditions have been completely abandoned in the analvses and one inappropriate matching condition used to be used at the elasricplastic boundary has been corrected. The reasonable solution of the plastic stresses near the crack line region has been established. BJJ matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary, the ptasric stresses. the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crack line region have been obtainedfor a mode I crack under uniaxial tension, as well as a mode I crack under biaxial tension, which shows that for both conditions the plastic stress components uV and cr.#, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same white the plastic stress fl., is different.

General forms of elastic-plastic matching equations for mode-III cracks near crack line

“…The authors proposed the crack line analysis method to address elastic-plastic crack problems [1][2][3][4][5][6][7] , which radically breaks through the traditional small-scale yielding conditions. The basic concept of the crack line analysis method lies in the following.…”

Study on Stress Solution Precision of the Plastic Range near Mode-I Crack Line under Unidirectional Uniform Stress

“…According to the analysis in the previous section, the left side of Tresca yield criterion expression is the same as that of Mohr-Coulomb yield criterion expression, literatures [4] and [5] only get a group of particular solutions with Tresca yield criterion and an incorrect 0 r expression through elastic-plastic boundary matching, which think that simply by equilibrium equation and yield criterion we cannot get the stress general solution of the plastic zone, the derivation in literature [6] and this paper's follow-up derivation prove that this conclusion is wrong, but the lack of (12c) ordinary differential equation derived by yield criterion in literature [6] causes the problem that first order power term and higher order terms in the stress general solution of the plastic zone derived do not fully satisfy the yield criterion, hereby we need to point out that both literatures [17] and [18] follow the derivation process of literature [5] respectively in the study on the damage of concrete micro-crack elastic and brittle static force under unidirectional tension and the study on the crack under internal pressure of rock mass joint, whose results are as unreasonable as that in literature [5].…”

“…Different from classical fracture theory which takes the stress field near the crack tip as the object of study, the analytical method of crack line field takes the stress field near the crack line as the object of study and solves the stress solution of the plastic zone through simultaneous equilibrium equation and selected yield criterion, which can effectively solve the problem that in a certain area near the crack line it is not restricted by small yield assumptions, and whose derivation process is of strict mechanical and physical significance, and in theory we can get infinitely precise solution of the whole crack elastic-plastic zone's stress values. As early as 1984, J. D. Aachenbach et al [1,2] first proposed the idea of line field analysis, in 1987, Guo Quanxin et al [3] developed this analytical method, and based on this, Yi Zhijian et al [4][5][6] proposed a complete line field analytical method, while Jian-hua Wang [7], , C. Guo [12], Y. X. Zhang [13], Guo JunHong [14], M. K. Huang [15], B. H. Zhang [16], et al developed research on theory and application with line field analytical method. Although the analytical method of crack line field, after thirty years of development, has made some valuable research achievements, there are still many problems not completely solved, limiting this method's development, application and promotion.…”

“…Although the analytical method of crack line field, after thirty years of development, has made some valuable research achievements, there are still many problems not completely solved, limiting this method's development, application and promotion. For problems of mode-I crack of infinite wide plate under unidirectional uniform stress, there are main research literatures including: literatures [4]~ [6] research ideal elastic-plastic materials with Tresca yield criterion; literature [18] researches the damage of concrete micro-crack elastic and brittle static force under unidirectional tension with Mohr-Coulomb yield criterion, of which literatures [4] and [5] only get a group of particular solutions for the stress field of the plastic zone and think that simply by equilibrium equation and yield criterion we cannot get the stress general solution of the plastic zone, literature [6] proves that this conclusion is wrong through derivation, but the lack of one ordinary differential equation derived by yield criterion in literature [6] causes the problem that first order power term and higher order terms in the stress general solution of the plastic zone derived do not fully satisfy the yield criterion, and the general solution is not precise enough; literatures [17] and [18] follow the derivation process of literature [5] with line field analytical method, whose results are as unreasonable as that in literature [5]; literatures [7][8][9][10][11]cite the plastic zone stress general solution in literature [6] in the study on a pair or two pairs of concentrated force with Tresca yield criterion, resulting in imprecise derivation results. For imprecise stress solution of the plastic zone near mode-I crack line of infinite wide plate under unidirectional uniform stress in above relevant research literatures, this paper, by virtue of Mohr-Coulomb yield criterion, will re-infer and solve the stress solution and the elastic-plastic boundary (scope of the plastic zone) of the plastic zone near the crack line satisfying equilibrium equation and yield criterion, solve the similarities and differences about the stress solution of the plastic zone with Tresca yield criterion and Mohr-Coulomb yield criterion under tension and press, and fully correct imprecise results about the stress solution of the plastic zone near mode-I crack line of infinite wide plate under unidirectional uniform stress.…”

Elasto-Plastic Fracture Analysis of Finite-Width Cracked Stiffened Plate

“…Because the boundary condition results in complexity to the elasto-plastic analysis for finite width cracked plates, the elasto-plastic field analysis remains one of the most difficult problems in elasto-plastic fracture analysis. Some research works [1][2][3][4][5][6] have fundamentally improved the line-field method to obtain exact solution of infinite width cracked plate. Without the small scale yielding condition, the method is very effective for the elastic-plastic analysis of finite width cracked plate.…”