ENG1011 Chap.8 Stress, Strain and Mechanical Properties
Stress, Strain and Mechanical Properties
Stress, Strain and Mechanical Properties is Week 5, where the unit turns from forces to the materials that carry them. Engineering stress is force divided by original cross-sectional area, and engineering strain is change in length divided by original length, so plotting one against the other describes the material independently of the specimen's size.
The straight first part of a tensile stress-strain curve is elastic, and its slope is the elastic modulus. Yield strength marks the start of permanent deformation, often found with a line offset by 0.2% strain where the knee is gradual. The highest point of the curve is the ultimate tensile strength, and multiplying it by the area gives the largest force a member can carry.
Ductility is the permanent strain at fracture, which is the fracture strain minus the elastic strain recovered when the load is released. The same elastic recovery fixes the final length of a bar loaded past yield and then unloaded.
A practical activity plots measured data in Excel and fits a trendline to the linear region for the modulus.
Week 5 is examined through numerical items built on a supplied stress-strain graph: reading the yield and ultimate strengths, estimating the modulus from the linear part, estimating ductility, and predicting the strain or final length for a given load. The repeater practice test shows each of these.
Reading values off a graph needs care with the axis units, which may be in percent strain or in megapascals.
What this chapter covers
- 01
Engineering stress and engineering strain
- 02
The tensile test and the stress-strain curve
- 03
Elastic modulus from the linear region
- 04
Yield strength and the 0.2% offset line
- 05
Ultimate tensile strength and maximum force
- 06
Ductility and elastic recovery
- 07
Final length after loading past yield
- 08
Selecting materials from their properties
Worked example · free
Stress, strain and extension of a steel rod
- 1Area: pi times 10 squared over 4 = 78.5 mm squared, so the stress is 5000/78.5 = 63.7 MPa.
- 1Strain: 63.7/200,000 = 0.000318, using E in MPa.
- 1Extension: 0.000318 times 2000 mm = 0.64 mm.
Key terms
- Engineering stress
- Force divided by the original cross-sectional area, measured in pascals or megapascals.
- Engineering strain
- Change in length divided by original length, a dimensionless ratio.
- Yield strength
- The stress at which permanent deformation begins, often found with a 0.2% offset line.
- Ultimate tensile strength
- The highest engineering stress on a tensile stress-strain curve.
- Ductility
- The permanent strain at fracture, usually expressed as a percentage.
- Elastic recovery
- The elastic strain that disappears when a load is removed, equal to stress divided by modulus.
Stress, Strain and Mechanical Properties FAQ
How is the elastic modulus found from test data?
Take the straight first part of the stress-strain curve and find its slope, stress change over strain change. In the unit's Excel plotting activity this is done by fitting a linear trendline to the data points in the linear region only.
Is ductility the strain at the fracture point on the graph?
Not exactly. The graph shows total strain while the load is applied. When the specimen breaks, its elastic strain springs back, so ductility is the fracture strain minus that elastic part, which is the fracture stress divided by the modulus.
What is the largest force a bar can carry in tension?
The ultimate tensile strength times the cross-sectional area. The repeater practice test finds the maximum tensile force this way, not from the yield strength, which instead marks when permanent deformation starts.
Why is stiffness different from strength?
Stiffness, measured by the elastic modulus, comes from how strongly atoms are bonded and governs how much a part stretches under load. Strength governs when it yields or breaks. Two materials can match in one and differ widely in the other.
How do I find the length after a bar is loaded beyond yield?
Subtract the elastic recovery, stress divided by modulus, from the total strain at the peak load to get the permanent strain, then multiply the original length by one plus that permanent strain.
Exam move
Practise reading every property from one plotted curve, then repeat with raw test numbers, so both question styles feel familiar. Keep a list of units beside you until N, mm and MPa are automatic. For selection questions, compare the deciding property in numbers before naming any other factor. Sketch a stress-strain curve from memory and label every property on it, including the unloading line after fracture.
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