Module 5: Mechanical Properties January 29, 2010

Transcription

1 Module 5: Mechanical Properties January 29, 2010 Module Content: 1. Mechanical properties of material are usually measured by a tensile test, and are usually presented in a stress-strain plot. 2. The stress-strain plot reveals parameters such as the elastic modulus, yield strength, ultimate strength, and energy parameter such as resilience and toughness. 3. The stress-strain curve also reveals a great deal about the tension/compression and ductile/ brittle behavior of materials. Module Reading, Problems, and Demo: Reading: Chapter 3 Problems: Prob. 3-5, 3-7 Demo: none Technology: MAE 2310 Str. of Materials E. J. Berger,

2 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

3 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

4 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

5 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

6 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

7 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

8 Concept: Determining Material Properties mechanical properties of materials are parameters like strength, failure characteristics, viscous characteristics, fracture properties, and the like a simple way of looking at these parameters is the tension test: MAE 2310 Str. of Materials E. J. Berger,

9 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

10 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

11 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

12 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

13 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

14 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

15 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

16 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

17 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

18 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

19 Theory: Stress-Strain Behavior because of the shape and size of the specimen, we can use average stress and average strain concepts to interpret the results of the test nominal average stress: σ = P A o original cross section nominal average strain: ɛ = δ L o original length MAE 2310 Str. of Materials E. J. Berger,

20 Ductile Steel is Great in Tension mild ductile steel MAE 2310 Str. of Materials E. J. Berger,

21 Ductile Steel is Great in Tension mild ductile steel MAE 2310 Str. of Materials E. J. Berger,

22 Ductile Steel is Great in Tension mild ductile steel MAE 2310 Str. of Materials E. J. Berger,

23 Ductile Steel is Great in Tension mild ductile steel MAE 2310 Str. of Materials E. J. Berger,

24 Concrete is Great in Compression concrete can carry very little load in tension MAE 2310 Str. of Materials E. J. Berger,

25 Concrete is Great in Compression concrete can carry very little load in tension MAE 2310 Str. of Materials E. J. Berger,

26 Concrete is Great in Compression concrete can carry very little load in tension MAE 2310 Str. of Materials E. J. Berger,

27 Rubber is Highly Nonlinear (Elastic!) sometimes we call nonlinear elasticity rubber elasticity MAE 2310 Str. of Materials E. J. Berger,

28 Rubber is Highly Nonlinear (Elastic!) sometimes we call nonlinear elasticity rubber elasticity MAE 2310 Str. of Materials E. J. Berger,

29 Theory: Brittle Materials brittle materials exhibit little or no plastic deformation before fracture MAE 2310 Str. of Materials E. J. Berger,

30 Theory: Hooke s Law Hooke s Law of linear elasticity simply states that in the elastic regime, stress and strain are linearly related, and that the constant of proportionality is a material parameter called the modulus of elasticity, or Young s modulus σ = Eɛ Young s modulus cannot exactly be predicted, but rather is measured through a tensile test Young s modulus is also (at least for steel), relatively insensitive to the carbon concentration and heat treatment of the steel from tensile test data, E is estimated from the quotient of proportional limit stress and proportional limit strain for steel, we almost always use a number like: E st = ksi = 210 GPa MAE 2310 Str. of Materials E. J. Berger,

31 Theory: Hooke s Law Hooke s Law of linear elasticity simply states that in the elastic regime, stress and strain are linearly related, and that the constant of proportionality is a material parameter called the modulus of elasticity, or Young s modulus σ = Eɛ Young s modulus cannot exactly be predicted, but rather is measured through a tensile test Young s modulus is also (at least for steel), relatively insensitive to the carbon concentration and heat treatment of the steel from tensile test data, E is estimated from the quotient of proportional limit stress and proportional limit strain for steel, we almost always use a number like: E st = ksi = 210 GPa MAE 2310 Str. of Materials E. J. Berger,

32 An Aside: The Titanic modern theories of why the Titanic was doomed after striking the iceberg nearly 100 years ago emphasize the metallurgy of the hull and rivet materials the composition of the steel used to construct the hull was a key player in the disaster--not the carbon content, but the sulphur content (which tends to make the steel brittle, especially in cold temperatures) hull buckling (from the Titanic historical society) MAE 2310 Str. of Materials E. J. Berger,

33 Theory: Yield Strength by Offset Method sometimes the yield strength of material is difficult to measure, that is, difficult to distinguish because the transition to plastic behavior is very smooth (e.g., aluminum) in this case, it is not uncommon to estimate the yield strength by an offset method, with 0.2% being a common choice MAE 2310 Str. of Materials E. J. Berger,

34 Theory: Yield Strength by Offset Method sometimes the yield strength of material is difficult to measure, that is, difficult to distinguish because the transition to plastic behavior is very smooth (e.g., aluminum) in this case, it is not uncommon to estimate the yield strength by an offset method, with 0.2% being a common choice smooth transition to plastic behavior, difficult to exactly determine the yield strength MAE 2310 Str. of Materials E. J. Berger,

35 Theory: Yield Strength by Offset Method sometimes the yield strength of material is difficult to measure, that is, difficult to distinguish because the transition to plastic behavior is very smooth (e.g., aluminum) in this case, it is not uncommon to estimate the yield strength by an offset method, with 0.2% being a common choice 0.2% offset, then use a line of slope E to intersect the experimental data and identify the yield strength MAE 2310 Str. of Materials E. J. Berger,

36 Theory: Yield Strength by Offset Method sometimes the yield strength of material is difficult to measure, that is, difficult to distinguish because the transition to plastic behavior is very smooth (e.g., aluminum) in this case, it is not uncommon to estimate the yield strength by an offset method, with 0.2% being a common choice 0.2% offset, then use a line of slope E to intersect the experimental data and identify the yield strength MAE 2310 Str. of Materials E. J. Berger,

37 Theory: Yield Strength by Offset Method sometimes the yield strength of material is difficult to measure, that is, difficult to distinguish because the transition to plastic behavior is very smooth (e.g., aluminum) in this case, it is not uncommon to estimate the yield strength by an offset method, with 0.2% being a common choice 0.2% offset, then use a line of slope E to intersect the experimental data and identify the yield strength MAE 2310 Str. of Materials E. J. Berger,

38 Theory: Energy Considerations work is the product of force and displacement in the direction of the force in deforming material, clearly work is done, and this work can be measured with a quantity called strain energy density, the energy associated with straining the material in terms of stress and strain: u = 1 2 σɛ = 1 2 Eɛ2 = 1 2 σ 2 E in our course, we talked about only two specific energy-related parameters: MAE 2310 Str. of Materials E. J. Berger,

39 Theory: Energy Considerations work is the product of force and displacement in the direction of the force in deforming material, clearly work is done, and this work can be measured with a quantity called strain energy density, the energy associated with straining the material in terms of stress and strain: u = 1 2 σɛ = 1 2 Eɛ2 = 1 2 σ 2 E in our course, we talked about only two specific energy-related parameters: resilience MAE 2310 Str. of Materials E. J. Berger,

40 Theory: Energy Considerations work is the product of force and displacement in the direction of the force in deforming material, clearly work is done, and this work can be measured with a quantity called strain energy density, the energy associated with straining the material in terms of stress and strain: u = 1 2 σɛ = 1 2 Eɛ2 = 1 2 σ 2 E in our course, we talked about only two specific energy-related parameters: resilience toughness MAE 2310 Str. of Materials E. J. Berger,