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In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing.〔("Toughness" ), (NDT Education Resource Center ), Brian Larson, Editor, 2001-2011, The Collaboration for NDT Education, Iowa State University〕 One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. It is also defined as a material's resistance to fracture when stressed. Toughness requires a balance of strength and ductility.〔 ==Mathematical definition== Toughness can be determined by integrating the stress-strain curve.〔 It is the energy of mechanical deformation per unit volume prior to fracture. The explicit mathematical description is: : where * is strain * is the strain upon failure * is stress Another definition is the ability to absorb mechanical energy up to the point of failure. The area under the stress-strain curve is called toughness. If the upper limit of integration up to the yield point is restricted, the energy absorbed per unit volume is known as the modulus of resilience. Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus of elasticity. That is, : Modulus of resilience = 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「toughness」の詳細全文を読む スポンサード リンク
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