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I Propagating Crack tip asymptotic field equations


: A [P () A s (port)] ~ orST (O) 'cited the following dimensionless equation (wall). (14) generation (9), with G () = 2Eg (n: Yan. R (19) 7 said that use different table style ● brother force should be% (≥ rr-style by the r0J Area = Pi plastic prison% often of several cut points ‰ hook revolves Chinese 88 - Harbin Engineering University Vol 19 one by one 2T + s S a G A: 0slnSill (+2 S) 1 a M2sin0) a cP + S) a sin0 (n +8 cosO) T + ~ 2M2sinOG One (1 a Shenzhen sjnOG ~ (20) s one of a 8T [(1 a M2sinZO) G +, etc. (1 A a) sin ‰ sOG】 _o (+ G) (1 a M2sin20) +2 ~ sin0 ( P + S) +2 (Ⅱ + ~ cos0) T a f a MnO ∞ sGr a 0si [12 口 G: 0 to consider the above equation is the exponential crack tip singularity field when asymptotic equation of the dynamic expansion. In order to with the quasi- compared to the static solution,[link widoczny dla zalogowanych], so that a O, then the above equation becomes Ssiu8-2Tsin0 + (d +8 cos0) S-aG = 0P: sin08Tsin6'++_+,[link widoczny dla zalogowanych]。 8cos0: 0 a + (n +) S for a total G: + ( 1 a) G +28 sin0 (P + S) +2 (n +8 cos0) T: 0 to L-type, the third type,[link widoczny dla zalogowanych], the fourth type, respectively, the derivative of 0, two and one can get P '% in8 +2 c0s A Psin0 a aT \) a 28sin0T = 0 【23) (21) and type (23) generation (22), after a complicated derivation after the availability of sin0 + a + (2 + c0s0] + P82si0 + Shan (2 + d) (n +8 cos0) a S3a = 0 【24) 4 quasi-static expansion of the asymptotic crack tip field equations for the quasi-static expansion of the stress function set (r.0), the stress-cho, expressed as ÷ + a (25) for incompressible Q condemnation plane strain and strain rate must also meet the following compatibility equation 3V + P (e) = O (26) where P (∈): ridicule a +({+{ a) a 2a, ({a) a 1V (+ le) + lr. a A = I1 ∞ No. 6 ? vibration and Qing: I Propagating Crack Tip Field Asymptotic Fang Chenggui aa from (+) + a + ∞) 1v2 (+ ∞) the equation (17), (1 generation (27), have been derived after the P (E delete 2P then from (25) vv available in = v (+) = 2 口 n even a [sin0 (P + P) + (total +2) cos0 ( + P)] Eq (2, (29) generation (26), available sin0 +[。+( a +2) cos0] + P8sin0 + P6 '(2 +) [Ⅱ +3 cos0] a S3a = 0 where 2ER0. 5 Results and conclusions (27) (2 (29) (30) (31) plastic material for the sticky problem of crack propagation. The derivation can be seen from the front. Equation (30) and type ( 24) is consistent with numerical results also prove this point. (1) through the analysis,[link widoczny dla zalogowanych], the power of the crack tip singularity of the dynamic solutions and quasi-static solution. (2) For I Propagating Crack. As sticky introduced. eliminate the plastic shock wave. and when characterization of crack Mach 10 speed, the dynamic solution can be subject to degradation, static solution. prove that the quasi-static solution is a special case of dynamic solutions. (3) used viscoplastic model to study aspects of the crack tip field is more reasonable and practical. References Gao Chen,[link widoczny dla zalogowanych], Han Bin Huang Kezhi. propagating crack in a quasi-static asymptotic solution of conflicts Mechanics, 1986.18 (1) :88-92 Kao Yu-Chen . dynamic crack tip plastic stick with a single parameter on Applied Mathematics and Mechanics 1990,11 (1) :33-43 THEORETICAL. visco-elastic plastic material moving Chi crack tip. Mechanics 1993,25 (2) :159-168GaoYC. Furtherstudyonstrainsin ~ tykIlaviorofmovingcracksinelashc-viscoplastlematerials.TheoreticalandAppendFractureMeehani ~ ~ 199014:233-242

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