Material Properties 3
Real Stress and Strain True M Corrected Stress M Engineering Strain
Several Alloys Material n MPa psi Low-carbon steel 0.26 530 77,000 (annealed) Alloy steel 0.15 640 93,000 (Type 4340, annealed) Stainless steel 0.45 1275 185,000 (Type 304, annealed) Aluminum (annealed) 0.20 180 26,000 Aluminum alloy 0.16 690 100,000 (Type 2024, heat treated) Copper (annealed) 0.54 315 46,000 Brass 0.49 895 130,000 (70Cu 30Zn, annealed) Source: From Manufacturing Processes for Engineering Materials by Seope Kalpakjian, 1997. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ. K
Problem A steel cylinder with an original diameter of 12.8 mm is tested under tension until fracture. The engineering fracture strength σf is found to be 460 MPa. If the cross sectional area at fracture is 10.7 mm calculate; The ductility in terms of area The true stress at fracture.
The ductility in terms of area
Ceramics Previously only really looked at metal cases
Mans first materials were ceramics in the form of stone Non metal solid inorganic
Mechanical Properties of Ceramics Possible cross sections F b d Rectangular Flexural strength Support Circular L 2 L 2 R = stress = Mc I where M = maximum bending moment c = distance from center of specimen to outer fibers I = moment of inertia of cross section F = applied load M c I Rectangular FL 4 d 2 bd 3 12 3FL 2bd 2 Circular FL 4 R R 4 4 FL R 3
40 250 200 30 Aluminum oxide Stress (MPa) 150 100 20 Stress (10 3 psi) 10 50 Glass 0 0 0 0.0004 0.0008 0.0012 Strain
Why So Brittle Bonds: Ceramics are held to gather by Ionic and covalent bonds (stronger than metallic bonds) The measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. Limited Slip system Stress raisers: The effect of a stress raiser is more significant in brittle than in ductile materials.
FIGURE 8.3 r s i f l gy w c r ill r isl c i i.
Hardness testing Measure of a materials resilience to plastic deformation. Mohs scale measures the ability to scratch a surface with one material on another (1- talc, 10- diamond).
Simple and inexpensive test, which can be performed on any sample. Non-destructive Can be used to infer other properties of the materials (i.e. other than hardness).
Rockwell Hardness test The system uses spherical tungsten carbide balls as indent ors sizes are (diameter) 1.588 mm 3.175 mm 6.350 mm 12.70 mm
Also used is the Brale, a conical diamond indenter
The Scales Table 7.5a Rockwell Hardness Scales Scale Symbol Indenter Major Load (kg) A Diamond 60 B in. ball 100 C Diamond 150 D Diamond 100 E in. ball 100 F in. ball 60 G in. ball 150 H in. ball 60 K in. ball 150 Table 7.5b Superficial Rockwell Hardness Scales Scale Symbol Indenter Major Load (kg) 15N Diamond 15 30N Diamond 30 45N Diamond 45 15T in. ball 15 30T in. ball 30 45T in. ball 45 15W in. ball 15 30W in. ball 30 45W in. ball 45
Other tests Table 7.4 Hardness Testing Techniques Shape of Indentation Formula for Test Indenter Side View Top View Load Hardness Number a Brinell 10-mm sphere P of steel or d tungsten carbide D d 2P HB D[D D 2 d 2 ] Vickers Diamond 136 d 1 d 1 P HV 1.854P/d 2 1 microhardness pyramid Knoop Diamond P HK 14.2P/l 2 microhardness pyramid l/b = 7.11 b/t = 4.00 Rockwell and Diamond 120 60 kg Superficial cone 100 kg Rockwell Rockwell,,, in. 150 kg diameter 15 kg steel spheres 30 kg Superficial Rockwell 45 kg t l b a For the hardness formulas given, P (the applied load) is in kg, while D, d, d 1, and l are all in mm. Source: Adapted from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior. Copyright 1965 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.
1000 800 600 200 300 400 100 80 60 40 20 Diamond 0 10 1 2 3 4 5 6 7 8 9 Talc Gypsum Calcite Fluorite Apatite Orthoclase Quartz Topaz Corundum or sapphire 10 5 20 50 100 200 500 1,000 2,000 5,000 10,000 Knoop hardness Brinell hardness Mohs hardness Rockwell C 110 0 20 40 60 80 100 Rockwell B Easily machined steels Nitrided steels File hard Cutting tools Most plastics Brasses and aluminum alloys
Questions on Material Properties Material Yield Strength! (MPa) Tensile Strength (MPa) Strain at Facture Fracture Strength! (MPa) Elastic Modulus (MPa) A 310 340 0.23 265 210 B 100 120 0.4 105 150 C 415 550 0.15 500 310 D 700 850 0.14 720 210 E Fractures Before Yielding 650 350 Which is hardest?