1 Stress and Strain An understanding of stress and strain is essential for the analysis of metal forming operations.Often the words stress and strain are used synonymously by the nonscientific public.In engineering usage,however,stress is the intensity of force and strain is a measure of the amount of deformation. 1.1 STRESS Stress o is defined as the intensity of force at a point. g=aF/8 A as A→0， (1.1) where F is the force acting on a plane of area,4. If the stress is the same everywhere in a body, G=F/A. (1.2) There are nine components of stress as shown in Figure 1.1.A normal stress component is one in which the force is acting normal to the plane.It may be tensile or compressive. A shear stress component is one in which the force acts parallel to the plane. Stress components are defined with two subscripts.The first denotes the normal to the plane on which the force acts and the second is the direction of the force.*For example,ox is a tensile stress in the x-direction.A shear stress acting on the x-plane in the y-direction is denoted by oy Repeated subscripts(e.g.)indicate normal stresses.They are tensile if both the plane and direction are positive or both are negative.If one is positive and the other is negative they are compressive.Mixed subscripts(e.g.,ox,oxy,oy=)denote shear stresses.A state of stress in tensor notation is expressed as Oxx Oyx Ozx Oij= Oxy Oyy Ozx (1.3) Oxz Oy 02z The use of the opposite convention should cause no problem because j=j.1 Stress and Strain An understanding of stress and strain is essential for the analysis of metal forming operations. Often the wordsstress and strain are used synonymously by the nonscientific public. In engineering usage, however, stress is the intensity of force and strain is a measure of the amount of deformation. 1.1 STRESS Stress σ is defined as the intensity of force at a point. σ = ∂F/∂ A as ∂ A → 0, (1.1) where F is the force acting on a plane of area, A. If the stress is the same everywhere in a body, σ = F/A. (1.2) There are nine components of stress as shown in Figure 1.1. A normal stress component is one in which the force is acting normal to the plane. It may be tensile or compressive. A shear stress component is one in which the force acts parallel to the plane. Stress components are defined with two subscripts. The first denotes the normal to the plane on which the force acts and the second is the direction of the force.∗ For example, σxx is a tensile stress in the x-direction. A shear stress acting on the x-plane in the y-direction is denoted by σx y . Repeated subscripts (e.g., σxx, σyy, σzz) indicate normal stresses. They are tensile if both the plane and direction are positive or both are negative. If one is positive and the other is negative they are compressive. Mixed subscripts (e.g., σzx , σx y , σyz) denote shear stresses. A state of stress in tensor notation is expressed as σi j = σx x σyx σzx σx y σyy σzx σx z σyz σzz , (1.3) ∗ The use of the opposite convention should cause no problem because σi j = σji . 1