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Questions and Answers
What does the term 'true strain' refer to in the context of material behavior?
What does the term 'true strain' refer to in the context of material behavior?
- The ratio of change in length to the original length.
- The ratio of lateral strain to axial strain.
- The natural logarithm of the ratio of final length to original length. (correct)
- The initial gradual increase in length during loading.
How is true stress calculated for a material under tension?
How is true stress calculated for a material under tension?
- True stress is the maximum load divided by the initial diameter.
- True stress is determined solely using the modulus of elasticity.
- True stress is the load divided by the area at the point of measurement. (correct)
- True stress is equal to external load divided by the original cross-sectional area.
Which characteristic differentiates ductile materials from brittle materials?
Which characteristic differentiates ductile materials from brittle materials?
- Brittle materials typically fail under tensile stress only.
- Ductile materials can absorb large energy before breaking. (correct)
- Brittle materials can undergo significant plastic deformation before failure.
- Ductile materials exhibit a linear elastic behavior until fracture.
In stress-strain analysis, what is typically represented by the slope of the linear portion of the curve?
In stress-strain analysis, what is typically represented by the slope of the linear portion of the curve?
Which of the following statements about elasticity and plasticity characteristics of materials is true?
Which of the following statements about elasticity and plasticity characteristics of materials is true?
What is the primary characteristic of ductile materials in tension?
What is the primary characteristic of ductile materials in tension?
How is the percent elongation of a material defined?
How is the percent elongation of a material defined?
What distinguishes brittle materials from ductile materials?
What distinguishes brittle materials from ductile materials?
What does the term 'offset yield stress' refer to?
What does the term 'offset yield stress' refer to?
In a stress-strain diagram for compression, which of the following is true?
In a stress-strain diagram for compression, which of the following is true?
Which type of elasticity describes materials that return to their original shape after unloading?
Which type of elasticity describes materials that return to their original shape after unloading?
What characterizes elastoplastic behavior in metals?
What characterizes elastoplastic behavior in metals?
Which of the following properties is NOT typically associated with materials like metals?
Which of the following properties is NOT typically associated with materials like metals?
What is the definition of true strain?
What is the definition of true strain?
How is true stress calculated for a material under load?
How is true stress calculated for a material under load?
Which property distinguishes ductile materials from brittle materials?
Which property distinguishes ductile materials from brittle materials?
In stress-strain analysis, what does the slope of the initial linear portion of the curve represent?
In stress-strain analysis, what does the slope of the initial linear portion of the curve represent?
When does a material exhibit plastic behavior?
When does a material exhibit plastic behavior?
What characteristic describes the elastic behavior of a material?
What characteristic describes the elastic behavior of a material?
How does the mechanical property of elasticity relate to stress-strain behavior?
How does the mechanical property of elasticity relate to stress-strain behavior?
What happens to the stress-strain curve of a ductile material when it undergoes strain hardening?
What happens to the stress-strain curve of a ductile material when it undergoes strain hardening?
Which standard is associated with determining mechanical properties of materials?
Which standard is associated with determining mechanical properties of materials?
What is the main reason for ensuring axial force acts through the centroid of a cross-sectional area in prismatic bars?
What is the main reason for ensuring axial force acts through the centroid of a cross-sectional area in prismatic bars?
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Study Notes
Aluminum Alloy Yield Stress
- Aluminum alloys do not have a distinct yield point.
- The transition from linear to non-linear behavior is gradual.
- Yield stress is determined using the offset method.
- A 0.2% offset is commonly used, resulting in "offset yield stress."
- Offset yield stress is slightly higher than the proportional limit.
Ductility
- Ductility in tension is characterized by elongation and reduction in area.
- Percent elongation is calculated by dividing the change in length by the original length and multiplying by 100%.
- Elongation is concentrated in the necking region, therefore, percent elongation depends on gage length and specimen dimensions.
- Percent reduction in area (RA) is calculated by dividing the difference between the original and final area by the original area and multiplying by 100%.
- A RA of greater than 50% signifies ductile steel.
- Materials with small fracture strain are classified as brittle, such as concrete, cast iron, rock, glass, etc.
Stress-Strain Diagram in Compression
- The stress-strain diagram for compression has different shapes compared to tension.
- The cross-section increases after yielding.
- Necking does not occur in compression.
Elasticity, Plasticity and Creep
- Linear elastic: stress and strain are directly proportional.
- Non-linear elastic: stress and strain are not directly proportional.
- Elastoplastic: the material behaves elastically up to the yield point, then exhibits plastic behavior. Most metallic materials behave this way.
- Creep: deformation over time under constant stress.
- Relaxation: stress decreases over time under constant strain.
- Other properties: fatigue strength, toughness, fracture toughness, notch toughness, resilience, etc.
Linear Elasticity, Hooke's Law and Poisson's Ratio
- Linear elastic behavior is characterized by direct proportionality between stress and strain.
- Homogeneous materials have uniform composition throughout.
- Isotropic materials have the same elastic properties in all directions.
- Hooke's Law states that stress is directly proportional to strain: σ = Eε
- E is the modulus of elasticity (Young's modulus).
- Values of E for different materials are listed in Appendix H.
- Poisson's ratio describes the lateral strain to axial strain in linear elastic materials.
- Lateral strain is typically negative, representing contraction.
- Poisson's ratio values for most materials are between 0.25 and 0.35.
Uniaxial Stress and Strain
- Uniaxial stress and strain occur in a prismatic bar when the loads act through the centroid of the cross-sections and the material is homogeneous.
- For uniform stress distribution, the axial force must act through the centroid of the cross-sectional area.
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