MSE200 Lecture 7 CH 6 2 6 4 Mechanical Properties I Instructor Yuntian Zhu Objectives outcomes You will learn the following Stresses and strains in solids Normal and shear stresses Elastic and plastic deformation The tensile test and the engineering stress strain curves Young s modulus the yield strength the ultimate tensile strength the percent elongation and percent reduction in area True stress and true strain Hardness and hardness testing http www mse ncsu edu zhu Materials Science Engineering Elastic and Plastic Deformation in Metals Elastic deformation Metal returns to its original dimension after the force is removed Plastic deformation The metal is deformed to such an extent such that it cannot return to its original dimension after the load is removed http www mse ncsu edu zhu Materials Science Engineering Engineering Stress and Strain under tension compression Engineering stress A0 Units of Stress are N m2 Pascals or Pa or PSI l A 0 0 Engineering strain 0 0 0 Force F N For elastic deformation E Young s modulus E is the http www mse ncsu edu zhu Materials Science Engineering Poissons Ratio Poissons ratio z 0 w0 y w y lateral longitudinal z w w0 0 Usually poissons ratio ranges from 0 25 to 0 4 Example Stainless steel Copper http www mse ncsu edu zhu Materials Science Engineering 0 28 0 33 Shear Stress and Shear Strain Shear stress S Shear force A Area of shear force application Tensile Shear Shear strain Shear Modulus G http www mse ncsu edu zhu Amount of shear displacement Distance h over which shear acts Materials Science Engineering Tensile test The most common test Strength of materials can be tested by pulling the metal to failure Load Cell Specimen Extensometer Force data is obtained from Load cell Strain data is obtained from Extensometer http video google com videosearch q tensile testing hl en emb 0 aq 0 oq tensile test http www mse ncsu edu zhu Materials Science Engineering Tensile Test Cont Round bar sample Flat sheet sample Commonly used Test specimen ASTM standard gives more information Typical Stress strain curve http www mse ncsu edu zhu Materials Science Engineering Young s Modulus Young s Modulus E Stress and strain are linearly related in elastic region Hooke s law Stress Linear portion of the stress strain curve E E The higher the bonding strength The higher the modulus of elasticity Largely determined by composition Insensitive to the grain size http www mse ncsu edu zhu Materials Science Engineering Strain Yield Strength 0 2 offset yield strength is that strength at which 0 2 plastic deformation takes place Construction line starting at 0 2 strain and parallel to elastic region is drawn to find 0 2 offset yield strength http www mse ncsu edu zhu Materials Science Engineering Ultimate tensile strength Ultimate tensile strength UTS is the maximum strength reached by the engineering stress strain curve Necking starts after UTS is reached Al 2024 Tempered More ductile the metal is more is the necking before failure True stress level at necking section S T R E S S MPa Necking Point Al 2024 Annealed Eng Strain http www mse ncsu edu zhu Engineering Stress strain curves of Al 2024 With two different heat treatments Ductile annealed sample necks more Materials Science Engineering Percent Elongation Ductility Percent elongation elongation to failure is a measure of ductility of a material It is the elongation of the metal before fracture expressed as percentage of original length Elongation to failure i e Ductility f l f l0 l0 http www mse ncsu edu zhu Materials Science Engineering Percent Reduction in Area Percent reduction area is also a measure of ductility Reduction Initial area Final area Area Initial area Ductile Brittle Percent reduction in area in metals decreases in case of presence of porosity http www mse ncsu edu zhu Materials Science Engineering True Stress True Strain True stress and true strain are based upon instantaneous cross sectional area and length F True Stress t Ai instantaneous area True Strain t li A0 Ln Ln l0 Ai t 1 http www mse ncsu edu zhu t ln 1 Materials Science Engineering Hardness and Hardness Testing http video google com videosearch q hardness testing hl en emb 0 aq 1 oq hardness Hardness is a measure of the resistance of a metal to permanent plastic deformation A quick way to estimate the yield strength 0 2 Hardness 3 General procedure Press the indenter that is harder than the metal Into metal surface Withdraw the indenter Measure hardness by measuring depth or width of indentation http www mse ncsu edu zhu Rockwell hardness tester Materials Science Engineering Home work Example Problems 6 4 6 5 6 6 6 7 6 8 Regular Problems Chapter 6 download from web Reading assignment section 6 5 6 8 http www mse ncsu edu zhu Materials Science Engineering