MSE 440

Mechanical Behavior of Metals

Res

erve

Lis

t

Course Objectives

In-depth examination of microscopic processes responsible for macroscopic mechanical behavior of metals;

Theories and models relating mechanical behavior to microstructures of metallic materials;

Failures of metals at elevated temperatures and under cyclic loads.

Annual World Consumption of Various Raw Materials, 2011

Billion Metric tons Billion m3 Cement 3.600 1.1 Roundwood 1.739 3.5 Industrial roundwood* 0.794 1.6 Steel 1.520 0.19 Plastics 0.280 0.31 Aluminum 0.044 0.01

* The difference between roundwood and industrial roundwood is wood used for fuel. Roundwood includes both fuelwood and wood used in construction, and for making paper, furniture, and other wood products. Source: Data for wood from FAO (2013); for cement, aluminum, and

steel from the U.S. Geological Survey (2013); and for plastics from the Association of Plastics Manufacturers in Europe (2013).

U.S. Demand for Selected Raw Materials, 1961 2012

Materials Used in Greatest Quantity (Million Metric Tons)

050

100150200250300350400450500

1961

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

2009

2012

TinNickelLeadZincCopperAluminumRaw SteelWoodCement

Source: U.S. Geological Survey, Commodity Summary Statistics (2013). Data for 2010-2011 wood consumption from UN, FAOStat Forestry (2013); 2012 est.

Great recession

I. CRYSTAL PLASTICITY

1. Theoretical Strength

2. Peierls-Nabarro Stress

h = a: distance between slip planes

: width of dislocation

: shear modulus : Poissons ratio b: Burgers vector of dislocation

2. Peierls-Nabarro Stress

3. Slip Systems :

FCC Structure

Basal Prismatic Pyramidal

4. Schmids Law Initial yield stress varies from sample to sample depending on the position of the crystal lattice relative to the loading axis.

It is the shear stress resolved along the slip direction on the slip plane that initiates plastic deformation. Yield will begin on a slip system when the shear stress on this system reaches a critical value (critical resolved shear stress, crss), independent of the tensile stress or any other normal stress on the lattice plane.

Experimental Validation of Schmids Law The experimental evidence of Schmids Law is that there is a critical

resolved shear stress. This is verified by measuring the yield stress of single crystals as a function of orientation. The example below is for Mg which is hexagonal and slips most readily on the basal plane (all other crss are much larger).

Soft orientation, with slip plane at 45to tensile axis

Hard orientation, with slip plane at ~90to tensile axis

= /coscos

Schmids Law: Example

Using Schmids Law:

5. Shear Stress Shear Strain Curves

A typical flow curve (stress-strain) for a single crystal shows three stages: - Stage I : easy glide with low hardening rates; - Stage II : with high, constant hardening rate, nearly independent of temperature or strain rate; - Stage III : with decreasing hardening rate and very sensitive to temperature and strain rate.

MSE 440Mechanical Behavior of MetalsSlide Number 2Course ObjectivesSlide Number 4Slide Number 5Annual World Consumption of Various Raw Materials, 2011U.S. Demand for Selected Raw Materials, 1961 2012Materials Used in Greatest Quantity(Million Metric Tons)Slide Number 8Slide Number 9I. Crystal PlasticitySlide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 194. Schmids LawSlide Number 21Slide Number 22Experimental Validation of Schmids LawSchmids Law: ExampleSlide Number 255. Shear Stress Shear Strain Curves