Explanation Given: Original diameter of steel ball is 40 mm . Hydrostatic pressure is 2 GPa . Concept used: Write the expression for total strain in sphere as per Hooke’s law. ε 1 + ε 2 + ε 3 = 1 − 2 v E ( σ 1 + σ 2 + σ 3 ) …… (1) Here, ε 1 , ε 2 and ε 3 are the strains in three direction for sphere , σ 1 , σ 2 and σ 3 are the stresses in all three directions, E is the modulus of elasticity of material and v is the Poisson ratio for material. For sphere which is subjected to hydrostatic pressure the magnitude of all three stresses will be same and magnitude of all three strains will be same. Substitute ε for ε 1 , ε for ε 2 , ε for ε 3 , − p for σ 1 , − p for σ 2 and − p for σ 3 in equation (1). ε + ε + ε = 1 − 2 v E ( − p − p − p ) 3 ε = 1 − 2 v E ( − 3 p ) Simplify above expression

Manufacturing Processes for Engineering Materials (6th Edition)

6th Edition

ISBN: 9780134290553

Author: Serope Kalpakjian, Steven Schmid

Publisher: PEARSON

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Chapter 2, Problem 2.79P

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Final diameter of solid steel ball.

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Chapter 2, Problem 2.78P

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Chapter 2 Solutions

Manufacturing Processes for Engineering Materials (6th Edition)

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Final diameter of solid steel ball.

Solution Summary: The author explains how to write the expression for total strain in sphere as per Hooke's law.

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