Stress Statemi@see.cn
Stress State mi@seu.edu.cn
ContentsTheStress State ofa Point（点的应力状态）·Simple,General&Principal StressState（简单、一般和主应力状态·OrderingofPrincipal Stresses（主应力排序）·On the DamageMechanisms of Materials（材料失效机制）·Plane Stress States（平面应力）·2-DCauchy'sRelation（平面柯西关系）·PlaneStressTransformation（平面应力转换）·Mohr's Circle（莫尔圆）·MaximumShearingStress（最大切应力）·Constructionof Mohr'sCircle（莫尔圆的构建）2
• The Stress State of a Point（点的应力状态） • Simple, General & Principal Stress State（简单、一般和主应力状 态） • Ordering of Principal Stresses（主应力排序） • On the Damage Mechanisms of Materials（材料失效机制） • Plane Stress States（平面应力） • 2-D Cauchy’s Relation（平面柯西关系） • Plane Stress Transformation（平面应力转换） • Mohr’s Circle（莫尔圆） • Maximum Shearing Stress（最大切应力） • Construction of Mohr’s Circle （莫尔圆的构建） Contents 2
Contents·3-DCauchy'sRelation（三维柯西关系）·StressTransformationofGeneral3-DStresses（空间应力转换）·ApplicationofMohr'sCirclein3-D（莫尔圆在三维应力状态中的应用）·GeneralizedHookesLaw（广义胡克定律）·TheRelationamongE,vandG（杨氏模量、泊松系数及剪切模量间的关系）·Fiber-reinforcedComposites（纤维增强复合材料）·Strain Energy Density under Generalized Stress States（一般应力状态下的应变能）·VolumeStrain,Mean Stress and Bulk Modulus（体应变、平均应力和体积模量）·Volumetric&DistortionEnergyDensity（体积应变能密度和畸变能密度）3
3 • 3-D Cauchy’s Relation（三维柯西关系） • Stress Transformation of General 3-D Stresses（空间应力转换） • Application of Mohr’s Circle in 3-D（莫尔圆在三维应力状态中的 应用） • Generalized Hooke’s Law（广义胡克定律） • The Relation among E, ν and G（杨氏模量、泊松系数及剪切模量 间的关系） • Fiber-reinforced Composites（纤维增强复合材料） • Strain Energy Density under Generalized Stress States（一般应力状 态下的应变能） • Volume Strain, Mean Stress and Bulk Modulus（体应变、平均应 力和体积模量） • Volumetric & Distortion Energy Density（体积应变能密度和畸变 能密度） Contents
The Stress State of a Point. The stress state at a point- is defined as the collection of the stress distributionson all planes passing through the point- can be analyzed via the stress distributions acting on adifferential cube, arbitrarily oriented with referencecoordinates. Method of differential cubes with:- infinitesimal side length- uniformly distributed stress on each of the six surfaces- equal and opposite stress on parallel sides4
• The stress state at a point - uniformly distributed stress on each of the six surfaces The Stress State of a Point - is defined as the collection of the stress distributions on all planes passing through the point. - can be analyzed via the stress distributions acting on a differential cube, arbitrarily oriented with reference coordinates • Method of differential cubes with: - infinitesimal side length - equal and opposite stress on parallel sides 4
Stresses on Obligue Planes. The stress distribution atLa point depends on theplane orientation alongwhich the point isexamined.=OCOS0Q0sin 2α25
F F A F F • The stress distribution at a point depends on the plane orientation along which the point is examined. 2 cos sin 2 2 Stresses on Oblique Planes 5