Engineering Plasticity

Theory and Applications in Metal Forming

Z. R. Wang, Weilong Hu, S. J. Yuan, Xiaosong Wang

• Publisher: Wiley
• Year: 2018
• Print ISBN: 9781119237303
• eBook ISBN: 9781119237327
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

An all-in-one guide to the theory and applications of plasticity in metal forming, featuring examples from the automobile and aerospace industries

• Provides a solid grounding in plasticity fundamentals and material properties
• Features models, theorems and analysis of processes and relationships related to plasticity, supported by extensive experimental data
• Offers a detailed discussion of recent advances and applications in metal forming

Chapter 1

1.1 Stress

1.1.1 The Concept of Stress Components

When a set of directional forces

acts on a deformable material element (see Figure 1.1) and remains balanced without causing a displacement and/or rotation, a set of balanced internal stresses must be generated because of the deformation taking place in the material element. Generally, if stress components distribute uniformly on a plane, the stress unit is equal to the force per unit area. Despite an inherent relation that exists between the stress and the acting force, the stress and the force are entirely different in their physical concepts that we could not confuse.

Figure 1.1 Directional forces acting on a unit element.

In analyzing displacement and rotation of a rigid body, all acting forces are vectors and can be converted into a single one. For example, the forces

shown in Figure 1.1 can be turned into a single vector P:

1.1

Equation (1.1) means that if

, this loaded body must move and if P does not pass the body's center, the body must rotate simultaneously.

However, it is incorrect to use the force P resulted from vector addition to analyze the elastic or plastic changes in shape of the material element. Different sets of directional forces will respond to different stress distribution on a plane cut out of this material element even if they have the same vector composition. Figure 1.2 illustrates the case of a simple uniaxial tension.

Figure 1.2 Relationship between forces and stresses on a plane cut out of a loaded body under uniaxial tension.

Stress components on different planes of this loaded material element are different. For example, the stress component on the plane vertical to the axis in Figure 1.2 can be expressed by

1.2

where P is the axial force, and S₀ is the cross section.

If this material element is a unit body with each edge equal to 1 unit, Equation (1.2) becomes

1.3

Equation (1.3) builds up a relationship between the force and the stre...

Table of contents

• Cover
• Title Page
• Copyright
• Table of Contents
• Preface
• Chapter 1: Fundamentals of Classical Plasticity
• Chapter 2: Experimental Research on Material Mechanical Properties under Uniaxial Tension
• Chapter 3: Experimental Research on Mechanical Properties of Materials under Non-Uniaxial Loading Condition
• Chapter 4: Yield Criteria of Different Materials
• Chapter 5: Plastic Constitutive Relations of Materials
• Chapter 6: Description of Material Hardenability with Different Models
• Chapter 7: Sequential Correspondence Law between Stress and Strain Components and Its Application in Plastic Deformation Process
• Chapter 8: Stress and Strain Analysis and Experimental Research on Typical Axisymmetric Plane Stress-Forming Process
• Chapter 9: Shell and Tube Hydroforming
• Chapter 10: Bulk Forming
• Chapter 11: Sheet Forming
• Index
• End User License Agreement