第25讲应力状态及强度理论11-1、2、3、4

1、韧性材料拉伸时为什韧性材料拉伸时为什么会出现滑移线？么会出现滑移线？低碳钢低碳钢铸铁铸铁20coscos p2sin2sin0 p单向应力状态低碳钢和铸铁的圆截面试件其扭转破坏的断口分别如图a及图b所示，试问为什么它们的断口形式不同？为什么脆性材料扭转时沿为什么脆性材料扭转时沿45螺旋面断开？螺旋面断开？(a)低碳钢低碳钢(b)铸铁铸铁纯剪切应力状态2sin2cos纯剪切应力状态xxxx y xxy根据微元根据微元 的局部平衡：的局部平衡： yx xyx y xxy yx xy根据微元根据微元 的局部平衡：的局部平衡： yxz x y z xy yx yz zy zx xz 3 32 21 1

2、 1、yxz x y z xy yx yz zy zx xz ( Plane State of Stresses )xyx y yx xyxyx yx xyxy( One Dimensional State of Stresses )( Shearing State of Stresses )三向应力状态三向应力状态平面应力状态平面应力状态特例特例特例特例Fl/2l/2Fl/2l/2S213aFzyzyFSyxzAFWTSt342 zzxWM 1 1 tWT 1 1 tWT 3 3 zyFSzyzzxWM 3 3 xyzxyaeaxyaeaeaea0 00 0 sin)sind(cos)sin

3、d(cos)cosd(sin)cosd(dAAAAAFyyxxxyn 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 0 00 0 cos)sind(sin)sind(sin)cosd(cos)cosd(dAAAAAFyyxxxytyx 9090 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 0 02 22 22 22 2 cossin xyyxddyxxytg 2 22 20 0 90900 00 0 2 22 22 22 2sincosxyyxyx 2 22 22 22 2xyyxyx )(minmax450

4、202)2arctan(210yxxyyx（D点在前半圆）点在前半圆） 2220)2arctan(21900yxxyyx（D点在后半圆）点在后半圆） 23220yxxy22tan0 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx )0 02 22 22 22 2 sincos xyyxddxyyx 2 22 21 1 tan 90901 11 1 2 22 22 2cossinxyyx 2 22 22 2xyyx )(minmaxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan 4 42

5、22 22 20 01 10 01 1 ,n3030efMPa.)sin()()cos(sincos3 358586060505060602 2606040402 2606040402 22 22 22 23030 xyyxyxMPa.)cos()()sin(cossin3 318186060505060602 2606040402 22 22 20 03030 xyyx1 16060404050502 22 22 20 0 )(tanyxxy20 0 5 567675 522220 0. x = -40MPa y =60 x = -50MPa =-30 MPa7 .

6、60MPa7 .80)2(222minmaxxyxyx MPa.MPa.7 760600 07 780803 32 21 1 1 yxxy 2 22 20 0tan 909090902 20 0 454545450 0 45 2 22 22 22 2xyyxyx)(minmax 1A alA50500 07070 xyyx ,4294291 10 0707050502 22 22 20 0.)(tan yxxy 5 562625 527270 0. xA A MPaMPa)(minmax969626262 22 22 22 2xyyxyx MPa,MPa96960 026263 32 21 1

7、 cossin sincos 2 22 22 22 22 22 22 2xyyxxyyxyx 2 22 22 22 22 22 2xyyxyx )()(),(0 02 2yxC 2 22 22 2xyyxR )(o xyD xyo o xy xA y yxD2 22 22 2xyyxR )(D xyo o xA y yxD2 22 21 12 21 1yxOBOAOBOAOBOC )()(2 22 22 22 22 2xyyxADCACD )(2 2yx D xyo o xA y yxDFxya )cos( 2 22 20 0CEOCCFOCOF 2 22 22 22 20 00 0sinsi

8、ncoscosCDCDOC 2 22 22 22 2sincosxyyxyx 2 22 22 22 22 22 20 00 0sincoscossin)sin(CDCDCEFEo 2 22 22 2cossinxyyxAB A1 12 22 21 11 12 22 2 max)(xyyxyxCAOCOA2 22 22 21 11 12 22 2 min)(xyyxyxCBOCOB 2D xyo o xA y yxDFB1A1D xyo o xA y yxD 2A1B1yxxyCADA 2 22 20 0)(tanyxxy 2 22 20 0tan)(tanyxxy 2 22 21 10 0D

9、xyo o xA y yxD 2A1B1G1G2max)( 2 22 21 12 2xyyxCGmin)( 2 22 22 22 2xyyxCG2 22 21 1 minmax ACB(-1,-0.2)DD(-0.4,0.2)ADC BD12015152709z250KN1.6m2mABC+200kN50kN+80kN.m250KN1.6m2mABCzIMy 4 46 63 33 31010888812122702701111111212300300120120mm zImm135 aydISFzzS* 3 32560002560005 57 71501501515120120mm).(* zaS12015152709zMPa.5 5122122 azcayIM MPa.*S6 66464 dISFzzaa a CAB(122.5 , 64.6)D(0 , - 64.6)A1 A2MPaMPa27271501502 22