文档介绍：应力强度因子第二章应力强度因子的计算--应力、位移场的度量的计算很重要,计算值的几种方法:KKK,:复变函数法、积分变换;:边界配置法、有限元法;:柔度标定法;:光弹性法.?2-1三种基本裂纹应力强度因子的计算一、无限大板?型裂纹应力强度因子的计算计算的基本公式,适用于?、?,,,lim2,,??,,“无限大”平板中具有长度为的穿透板厚的裂纹表面上,距离处2axb,,,yyppxbppaa,ReImZyZ,,,x??,,ReImZyZ,,y??,,yZRe,,xy?选取复变解析函数:222pzab,Z,22,()zb,边界条件:a..z,,,,,,0,,,。za,,,,,,0,0zb,,,在轴所在截面上内力总和为。xypx1以新坐标表示:222()paab,,,Z,22[()](2),,,aba,,,,2pa,,,,,,,KZlim2()?22,,0,()ab,,具有长度为的穿透板厚的裂纹表面上,在距离的xa,,,yqxq2a1利用叠加原理:2qa微段集中力qdx,,,dKdx?22,,()axa2qa,,Kdx?,220,,()ax22令,xaaxa,,,,coscos,,dxad,cos,,,1a1sin()aaacos,a,1a1,,,Kqdq22sin(),a?,0acos,,,当整个表面受均布载荷时,.aa,1a,1a,,2sin(),,Kqqaa?,,在轴上有一系列长度为,,,aaxbbb,边界条件是周期的:.,,,,,,,,,,,,,,,,,0,,22,,,,0,,,,y单个裂纹时,z,Z22,za又Z应为的周期函数2b,zsin,2bZ,,za,,22(sin)(sin),22bb采用新坐标:,,,za,sin(),a,,2bZ,,(),aa,,,22(sin)(sin),22bb,,,当,,0时,sin,cos1,,,,,222bbb,,,,,sin()sincoscossin,,,aaa,,,,22222bbbbb3,,,,,cossinaa,222bbb,,,,,,,2222[sin()]()cos2cossin(sin),,,,aaaaa,,,2222222bbbbbbb,,,,,22,,,,[sin()](sin)2cossinaaaa,,22222bbbbb,asin,2b,,Z,,02aa,,,,cossin222bbb,asin,a,2b,,,,KZblim22tan,,,?,,02b1aa,,cossin222bbb2ba,,atan,,ab2,2ba,取------修正系数,大于1,,Mtanw?ab2,21a若裂纹间距离比裂纹本身尺寸大很多()可不考虑相互作用,按单个裂纹,、无限大平板?、?型裂纹问题应力强度因子的计算1.?型裂纹应力强度因子的普遍表达形式(无限大板):KZ,lim()2,,,?,,,,aax,bbb,4,zsin,2bZz(),za,,22(sin)(sin),22bb,sin(),a,,2bZ(),,a,,22[sin()](sin),,a,22bb2ba,,,,KZalim2()tan,,,,,?,,0ab2,3.?型裂纹应力强度因子的普遍表达形式(无限大板):KZ,lim2(),,,?,,:2ba,,Katan,,ab2,5?2-2深埋裂纹的应力强度因子的计算yx,x2a,zz2c,1950年,格林和斯内登分析了弹性物体的深埋的椭圆形裂纹邻域内的应力和应变,得到椭圆表面上任意点,沿方向的张开位移为:y122xz2yy,,,(1)022ac22(1),,,a其中:.y,0E,,,22ca,22(于仁东书),,,1sind,,,20a1,2a2222(王铎书),,[sin()cos],,,d,0c1962年,Irwin利用上述结果计算在这种情况下的应力强度因子x,pra,czcOa6原裂纹面zx,,,,,,cos,sin11又22xz22222211,,,,,1cxazac1122acac,,,2222casincos,,,假设:椭圆形裂纹扩展时,其失径的增值r与成正比.,,(f远小于1)rf,,rr2222,,,,fcasincos,,ac,