2: Tensile Tests

Overview of Plastic Deformation in Tensile Testing

• Understanding plastic deformation in tensile test samples, specifically the dog bone sample shape.

Deformation Observation

• Visualizing deformation: Original positions of marked stripes on the sample indicate deformation during loading.

• As load increases, constraining plate fixes the bottom, leading to upward displacement of the sample.

Strain and Displacement

• The graph during tensile testing clearly highlights where plastic deformation occurs.

• Displacement observed in higher stripes indicates upper sections are deforming more significantly.

• Strain measures relative displacement, comparing original and current positions.

Engineering Stress and Strain

• Engineering stress (C3_e) is defined as force divided by original cross-sectional area (A_0).

• Engineering strain (B5_e) is measured as change in length (ΔL) over original length (L_0).

• Initial stress-strain curves show maximum stress and failure points based on original measurements.

True Stress and True Strain

• True stress reflects current cross-sectional area during plastic deformation, which decreases as material stretches.

• True stress is defined as force divided by current cross-section, yielding higher values than engineering stress.

• True strain is represented as natural log of current length (L) over original length (L_0) and correlates to engineering strain by the relation:B5_{true} = ln(1 + B5_e)

Differences in Stress-Strain Curves

• Engineering and true stress-strain curves exhibit different shapes:

  • True stress vs. true strain does not show the same maximum as engineering stress vs. engineering strain due to continuous strengthening.

  • The transition between elastic and plastic regions shows different interpretations, particularly for defining yield strength.

Defining Yield Strength

• The offset method (0.2% offset) is used to identify yield strength, creating a parallel line off the linear range to intersect at plastic deformation onset.

• Yield strength can be defined using either engineering or true stress-strain curves.

Dislocations and Work Hardening

• Plastic deformation in metals involves dislocation movement, causing resistance to further deformation due to increased dislocation density.

• The increase in dislocation entangles the material, requiring more force to continue deforming, leading to work hardening.

Necking Phenomenon

• As deformation continues, necking may occur when local cross-sectional area reduces significantly, leading to concentrated stress.

• The neck region can be stable if work hardening compensates for stress increases; otherwise, failure may initiate there.

Failure Mechanisms

• Failure occurs when high stress levels result in bond breaking in local neck regions, where cracks may propagate leading to complete material failure.

• Understanding the nature of fractures helps in analyzing tensile test outcomes, especially during rapid loading conditions.

Summary of Experiment

• The dog bone sample's behavior during tensile tests illustrates principles of elasticity, yield strength, plastic behavior, necking, and eventual failure.

• Observations inform future lectures on mathematical modeling and the mechanics of material deformation.