[{"data":1,"prerenderedAt":37},["ShallowReactive",2],{"topic-en-strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Ftensile-test-diagram-characteristic-points":3},{"topic":4,"trail":18,"children":32,"tasks":33,"alternates":34},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},110,"Tensile Test Diagram and Characteristic Points","en","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Ftensile-test-diagram-characteristic-points","Tensile Test Diagram — Characteristic Points and Regions","Tensile stress–strain diagram: elastic and plastic regions, proportional, yield and ultimate strengths, necking, and specimen fracture.","This topic explains the engineering tensile stress–strain diagram and the physical meaning of its characteristic regions and points. It covers proportional and elastic behavior, yield strength, ultimate tensile strength, plastic deformation, necking, and fracture, helping students interpret tensile-test results for engineering calculations.","\u003Cp>A tensile-test diagram shows the relationship between stress and strain of a specimen during loading. Its shape is used to determine important elastic, ductility, and strength characteristics of a material.\u003C\u002Fp>\u003Ch2>Main regions\u003C\u002Fh2>\u003Cp>At the beginning of loading, deformation is predominantly elastic, and within the proportional region stress is approximately linearly related to strain.\u003C\u002Fp>\u003Cdiv class=\"formula-chunk\">\u003Cp>Within the linear-elastic range, normal stress is proportional to axial strain:\u003C\u002Fp>\u003Cp>$$\\sigma=E\\varepsilon.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$\\sigma$\u003C\u002Fstrong> — normal stress, Pa or MPa;\u003C\u002Fli>\u003Cli>\u003Cstrong>$E$\u003C\u002Fstrong> — Young's modulus, Pa or MPa;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\varepsilon$\u003C\u002Fstrong> — axial strain, dimensionless.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The law applies to the linear portion of the stress–strain curve while $\\sigma$ and $\\varepsilon$ remain proportional.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>\u003Cp>After the material leaves the elastic range, irreversible plastic deformation develops. For ductile metals, the yield strength or offset yield strength is identified, while the maximum engineering stress is called the ultimate tensile strength.\u003C\u002Fp>\u003Ch2>After the maximum load\u003C\u002Fh2>\u003Cp>In a ductile specimen, localized reduction of cross-section called \u003Cstrong>necking\u003C\u002Fstrong> may occur. Further deformation concentrates in this region and eventually ends in fracture. The exact diagram shape and prominence of individual regions depend on the material and test conditions.\u003C\u002Fp>\u003Ch2>Engineering significance\u003C\u002Fh2>\u003Cp>The diagram is used to assess stiffness, the onset of plastic deformation, strength, and the ability of a material to deform before fracture. These characteristics support material selection and the determination of allowable stresses.\u003C\u002Fp>",[14],{"id":15,"code":16,"type":17,"locale":7},68,"uniaxial-hooke-law","formula",[19,23,27,31],{"id":20,"name":21,"path":22},45,"Strength of Materials","strength-of-materials",{"id":24,"name":25,"path":26},46,"Tension and Compression","strength-of-materials\u002Ftension-and-compression",{"id":28,"name":29,"path":30},48,"Mechanical Properties of Materials","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials",{"id":5,"name":6,"path":8},[],[],{"en":35,"uk":36},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Fstrength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Ftensile-test-diagram-characteristic-points","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fopir-materialiv\u002Froztyah-i-stysk\u002Fmekhanichni-vlastyvosti-materialiv\u002Fdiagrama-roztiahu-ta-kharakterni-tochky",1787712538962]