Class #1.2 Civil Engineering Materials – CIVE 2110 Strength of Materials Mechanical Properties of Materials Fall 2010 Dr. Gupta Dr. Pickett

Stress and Strain Mechanical Properties of Materials - used to develop relationships between Stress and Strain. - determined Experimentally.

Experimental Determination of Mechanical Properties of Materials Stress and Strain experiments: A standard specimen of the Material: - Pulled in Uniaxial Tension. - Diameter = 0.5 in. - Gauge Length = 2.0 in. Or - a strain gauge is placed parallel to long axis of specimen

Stress-Strain Diagrams P Conventional Stress-Strain Diagram : Normal Stress calculated using ORIGINAL cross sectional area, AO. Called Engineering Stress. Even though cross section decreases, necks down. Assumes stress is CONSTANT over cross section. Normal Strain calculated using ORIGINAL length, LO. Assumes strain is CONSTANT over cross section P P

Stress-Strain Diagrams P TRUE Stress-Strain Diagram : Normal Stress calculated using ACTUAL cross sectional area, Ai, at any instant. Called TRUE Stress. Because cross section decreases, necks down. Normal Strain calculated using ACTUAL length, Li , at any instant. P P

Stress-Strain Diagram – Ductile Material Conventional (Engineering) and TRUE Stress-Strain diagrams Differ only in regions of LARGE strain . σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - Label the axes. - REGIONS: - Elastic – region where specimen will return to original size & shape after loading & unloading - Plastic - region where specimen will NOT return to original size & shape after loading & unloading - Yielding – region where specimen will continue to elongate with little or no increase in load σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - REGIONS: - Strain Hardening – region where specimen will elongate only with increasing load, and the cross sectional area will decrease uniformly over entire specimen gauge length - Necking - region where specimen cross sectional area will decrease in a localized spot, and load carrying capacity will decrease, uncontrollably σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - POINTS: - Proportional Limit, σPL – highest stress at which Stress and Strain are linearly proportional, via E - Modulus of Elasticity (Young’s Modulus) – the slope of the Stress-Strain curve in the Linear-Elastic region, slope up to σPL (ESTEEL=29x106 psi) E=Δσ/Δε σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - POINTS: - Modulus of Elasticity (Young’s Modulus) the slope of the Stress-Strain curve in the Linear-Elastic region, slope up to the Proportional Limit (ESTEEL=29x106 psi) - Hooke’s Law E=Δσ/Δε σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - POINTS: - Modulus of Elasticity (Young’s Modulus) = the slope of the Stress-Strain curve in the Linear-Elastic region - alloy content affects - Proportional Limit - not Modulus of Elasticity (ESTEEL=29x106 psi) E=Δσ/Δε E=Δσ/Δε σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - POINTS: - Elastic Limit, σEL – highest stress at which the specimen will return to original size and shape after loading and unloading (Steel, very close to Proportional Limit) - Yield Point, σY – stress at which specimen will have permanent (plastic) deformation after loading & unloading, specimen will elongate with LITTLE or NO load increase (Steel, very close to Proportional Limit) E=Δσ/Δε σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - POINTS: - Ultimate Stress, σU – highest stress on the specimen - Fracture Stress, σF – stress at which specimen breaks E=Δσ/Δε σ (KSI) ε (μ in./in.)

Stress-Strain Diagram – Ductile Material Engineering Stress-Strain diagrams: - DUCTILE vs. BRITTLE Behavior: - Ductile behavior – specimen exhibits significant permanent (plastic) deformation before failure, (good, gives warning before failure) - Brittle behavior – specimen exhibits little or no permanent (plastic) deformation (bad, no warning before failure) E=Δσ/Δε σ (KSI) ε (μ in./in.)

Engineering Stress-Strain Diagram – Ductile Some Ductile materials have distinct Yield Point and large yielding region: - alloys such as; steel, brass, - elements such as; Molybdenum, Zinc no distinct Yield Point: - Such as; Aluminum - need to define a YIELD STRENGTH - Stress at 0.2% strain - draw a line from ε = 2000x10-6 = 0.002 = 0.2% - parallel to the linear elastic portion of curve - σYS = stress at intersection of parallel line with curve E=Δσ/Δε σ (KSI) ε (μ in./in.) ε (μ in./in.)

Engineering Stress-Strain Diagram – Brittle Brittle materials exhibit LITTLE or NO permanent deformation BEFORE failure (BAD). Examples: - Gray Cast Iron - Concrete - Low Tensile Strength - High Compression Strength - No failure warning (Tension or Compression) - BAD - need to get people - off bridge - out of building E=Δσ/Δε ε (μ in./in.) σ (KSI)

Brittle - Concrete Concrete - Low Tensile Strength - High Compression Strength - No failure warning (Tension or Compression) - BAD - need to get people - off bridge - out of building

Brittle - Concrete Concrete - Low Tensile Strength - High Compression Strength - No failure warning (Tension or Compression) - BAD - need to get people - off bridge - out of building

Ductility DUCTILITY can be measured by: - Percent Elongation: - Percent Reduction of Area: E=Δσ/Δε ε (μ in./in.) σ (KSI)

Strain Hardening & Hysteresis If a specimen is loaded past σEL, Then unloaded, Some deformation will be removed, Some deformation will remain. The slope of the UNLOADING curve will be the SAME SLOPE, E, as the LOADING curve. If specimen is loaded again, The slope of the re-load curve will be E. A higher σY will be reached because of STRAIN HARDENING. But there will be a smaller plastic region Remaining, So DUCTILITY will be less. E=Δσ/Δε ε (μ in./in.) σ (KSI) Original Yield Point Yield Point after Strain Hardening

Strain Hardening & Hysteresis Some energy will be LOST or USED or DISSIPATED In the LOAD and UNLOAD processes. Energy dissipated is a function of the area inside the LOAD-UNLOAD curves, called HYSTERESIS loops. Mechanical hysteresis devices are used to Reduce EARTHQUAKE forces on structures.

Hysteresis Devices

Hysteresis Devices

Stress -Strain Diagrams Example: Problem 3-4 Hibbeler 7th edition, pg. 102

Stress -Strain Diagrams Example: Problem 3-4 Hibbeler 7th edition, pg. 102