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Chapter 2: Mechanical Behavior, Testing, and Manufacturing Properties of Materials

2.1 Introduction

  • This chapter examines the effects of external forces on material behavior and the testing methods used to determine mechanical properties.
  • Forming operations create parts by applying external forces using tools and dies, applicable to both metallic and nonmetallic materials.
  • Common examples include:
    • Forging turbine disks
    • Extruding aluminum components
    • Drawing wire for nails
    • Rolling metal sheets for appliances
  • Operations can occur at room temperature or elevated temperatures and varying rates of deformation.
  • A variety of metallic and nonmetallic materials with distinct properties and characteristics are utilized.
  • The chapter focuses on mechanical properties relevant to design and manufacturing, including common testing methods.

2.2 Tension

  • Tension Test: Most common method for determining mechanical properties such as strength, ductility, and toughness.
  • Test specimen preparation follows American Society for Testing and Materials (ASTM) specifications, typically a cylindrical shape with:
    • Original gage length, $l_0$ = 50 mm
    • Cross-sectional area, $A_0$ = 12.5 mm diameter
2.2.1 Stress-Strain Curves
  • Engineering Stress (σ): Ratio of applied load ($P$) to the original cross-sectional area ($A_0$).
    • Formula: extσ=PA0ext{σ} = \frac{P}{A_0}
  • Engineering Strain (e): Ratio of instantaneous length to original gage length.
    • Formula: e=l−l<em>0l</em>0e = \frac{l - l<em>0}{l</em>0}
  • Typical tension test sequence shows:
    • Initially, linear elastic behavior correlates with hooke's law.
    • Upon reaching the yield stress ($S_y$), permanent deformation occurs.
    • Maximum engineering stress reached at ultimate tensile strength ($S_{ut}$).
  • A true stress formulation captures actual conditions as cross-sectional area changes with deformation:
    • extTruestress=PAext{True stress} = \frac{P}{A}
  • The true strain is calculated as:
    • extTruestrain=extlnll0ext{True strain} = ext{ln}\frac{l}{l_0}
  • True stress-true strain relationships reflect plastic deformation and energy requirements for reshaping materials.
2.2.2 Ductility
  • Ductility: Measure of plastic deformation before fracture. Common measures of ductility include:
    • Total elongation (%): extElongation=l<em>f−l</em>oloimes100ext{Elongation} = \frac{l<em>f - l</em>o}{l_o} imes 100
    • Reduction of area (%): extReductionofarea=A<em>o−A</em>fAoimes100ext{Reduction of area} = \frac{A<em>o - A</em>f}{A_o} imes 100
2.2.3 True Stress and True Strain
  • True Stress (στ): extTruestress=PAext{True stress} = \frac{P}{A} where $A$ is the instantaneous area.
  • True Strain (€): Calculated through incremental elongation:
    • €=extlnll0€ = ext{ln}\frac{l}{l_0}
2.2.4 Construction of Stress-Strain Curves
  • Engineering stress-strain curves derived from load-elongation graphs, capturing elastic and plastic behaviors.
  • For true stress-true strain curves, adjustments made for necking yield higher stress values.
  • Relationships defined by the equation:
    • extσ=K€next{σ} = K €^n
2.2.5 Strain at Necking in a Tension Test
  • The strain at necking correlates with the strain-hardening exponent ($n$) of the material, impacting behaviors like sheet-metal forming.
2.2.6 Temperature Effects
  • Temperature increases ductility and toughness while decreasing yield strength and elastic modulus.
2.2.7 Effects of Rate of Deformation and Strain Rate
  • Deformation Rate: Speed of applying force; Strain Rate: Change of length relative to original length.
  • Affects tensile properties significantly due to plasticity from high temperatures, increasing strain-rate hardness.
2.2.8 Hydrostatic Pressure Effects
  • Hydrostatic pressure tests indicate increases in strain at fracture for both ductile and brittle materials.
2.2.9 Radiation Effects
  • Radiation exposure leads to changes in mechanical properties, including yield strength and ductility.

2.3 Compression

  • Compression tests provide essential information for processes like forging and rolling. Friction impacts the stress-strain curve, complicating results.
  • Bauschinger Effect: Lower yield strengths during subsequent compression after tensioned plastic deformation.
Disk Test for Brittle Materials
  • Disk Test: Used for brittle materials; calculates tensile stresses during diametral compression using:
    • σ=2Pextπdtσ = \frac{2P}{ ext{π}dt}

2.4 Torsion

  • Torsion tests apply shear strains to tubular specimens, evaluating shear stress as:
    • T=T2extπr2tT = \frac{T}{2 ext{π}r^2t}
  • Shear strain given by:
    • extγ=θLLext{γ} = \frac{θL}{L} where θ is the angle of twist.

2.5 Bending (Flexure)

  • Bending tests measure longitudinal stresses and predict fracture strains for brittle materials through three-point or four-point tests, analyzing moments.

2.6 Hardness

  • Hardness: Measured resistance to permanent indentation, indicative of strength and wear resistance. Various hardness tests exist:
  • Brinell Test: Measures diameter of indentation from a steel ball under load.
  • Rockwell Test: Compares penetration depth under varying loads.
  • Vickers and Knoop Tests: Employ diamond indenters for precision in small specimen hardness measurement.
Hardness-Strength Relationships
  • Hardness can be correlated with yield strength; typically, it's approximately three to five times the yield strength.

2.7 Fatigue

  • Fatigue failure occurs under fluctuating loads, resulting in cracks initiating from defects, leading to fractures occurring below static load limits.
  • S-N Curves: Plot average stress vs cycles to identify fatigue limits and material endurance properties.

2.8 Creep

  • Creep: Permanent deformation under sustained load, crucial in high-temperature applications. Examined through a creep test assessing changes over time.
    • Characteristic curve consists of primary, secondary, and tertiary stages leading to fracture.

2.9 Impact

  • Impact tests determine material toughness under sudden loading, assessing dynamic resistance and ductility transitions in materials.

2.10 Failure and Fracture of Materials

  • Failure: Two main categories are fractures (ductile and brittle) and buckling. Understanding material failure is key in material selection and processing.
  • Ductile Fracture: Involves plastic deformation preceding failure, characterized by void formation.
  • Brittle Fracture: Occurs with minimal deformation and propagates along cleavage planes.
Fatigue Fracture
  • Cycle-induced cracks propagate until fracture; surface conditions greatly affect fatigue life.

2.11 Residual Stresses

  • Residual stresses remain after shaping every part, influencing fatigue life, fracture strength, and overall performance.

2.12 Work, Heat, and Temperature

  • Mechanical work transforms into heat during deformation, influencing temperature calculations per material properties.
  • Energy considerations are critical for predicting heat management in manufacturing processes, impacting property retention in materials.

Summary

  • Mechanical properties such as strength, ductility, and toughness are integral to design processes. The tensile test serves as the standard method to determine these properties, further analyzed through derived stress-strain relationships.