Mechanical Behavior, Testing and Manufacturing Properties of Materials Strength Hardness Toughness Stiffness Strength/Density

Tension test Specimen can be round, flat or tubular ASTM specifications Stress-Strain Curve Elastic region Plastic region Necking

Tension test formulas  

Hooke’s law  

FIGURE 2.1 (a) A standard tensile-test specimen before and after pulling, showing original and final gage lengths. (b) Stages in specimen behavior in a tension test.

FIGURE 2.2 A typical stress–strain curve obtained from a tension test, showing various features.

Plastic deformation Proportional limit – the stress that the specimen undergoes nonlinear elastic deformation Permanent(plastic) deformation – occurs when the yield stress of the material is reached Y(yield stress) is often determined using the offset method (.2% elongation) figure 2.2

FIGURE 2.3 Schematic illustration of the loading and the unloading of a tensile-test specimen. Note that, during unloading, the curve follows a path parallel to the original elastic slope.

Ultimate tensile strength The maximum engineering stress is called the tensile strength or ultimate tensile strength and is the maximum stress found from the σ-ε diagram

TABLE 2.2 Mechanical Properties of Various Materials at Room Temperature

ductility  

FIGURE 2.5 (a) Load–elongation curve in tension testing of a stainless steel specimen. (b) Engineering stress–engineering strain curve, drawn from the data in Fig. 2.5a. (c) True stress–true strain curve, drawn from the data in Fig. 2.5b. Note that this curve has a positive slope, indicating that the material is becoming stronger as it is strained. (d) True stress–true strain curve plotted on log–log paper and based on the corrected curve in Fig. 2.5c. The correction is due to the triaxial state of stress that exists in the necked region of the specimen.

True stress & true strain  

TABLE 2.3 Typical Values for K and n for Metals at Room Temperature

Strain at necking in a tension test The true strain at the onset of necking is numerically equal to the strain-hardening exponent, n, of the material. Thus, the higher the value of n, the higher the strain that a piece of material can experience before it begins to neck. Note: from table 2.3 these have high n values and can be stretched uniformly to a greater extent than can the other metals listed. Annealed copper Brass Stainless steel

FIGURE 2.6 True stress–true strain curves in tension at room temperature for various metals. The curves start at a finite level of stress: The elastic regions have too steep a slope to be shown in this figure; thus, each curve starts at the yield stress, Y, of the material.

Temperature effects Increasing the temperature… Ductility increases Toughness increases Yield stress decreases Modulus of elasticity decreases n decreases (strain-hardening exponent)

FIGURE 2.7 Effect of temperature on mechanical properties of a carbon steel. Most materials display similar temperature sensitivity for elastic modulus, yield strength, ultimate strength, and ductility.

Deformation rate Deformation rate is defined as the speed at which a tension test is being carried out (ft/min, m/sec…) Strain rate is a function of the specimen’s length. A short specimen elongates proportionally more during the same period than does a long specimen. Superplasticity refers to the capacity of some materials to undergo large uniform elongation prior to necking and fracture in tension (examples: bubble gum, glass, thermoplastics at room temperature)

Compression test Solid cylindrical specimen between two well lubricated flat dies (platens) Because of friction between the specimen and the platens, the specimen’s cylindrical surfaces bulge (barreling) Slender specimens buckle For ductile materials, the true stress-true strain curves coincide Brittle materials are generally stronger and more ductile in compression Disk test is also used to test compressive stress

FIGURE 2.9 Disk test on a brittle material, showing the direction of loading and the fracture path.

torsion  

FIGURE 2.10 A typical torsion-test specimen; it is mounted between the two heads of a testing machine and twisted. Note the shear deformation of an element in the reduced section of the specimen.

Bending (flexure) Used for brittle materials Three point or four point Rectangular cross section specimens Modulus of rupture is the stress at fracture

FIGURE 2.11 Two bend-test methods for brittle materials: (a) three-point bending; (b) four-point bending. The areas on the beams represent the bending moment diagrams, described in texts on the mechanics of solids. Note the region of constant maximum bending moment in (b); by contrast, the maximum bending moment occurs only at the center of the specimen in (a).

hardness Defined as the resistance to permanent indentation Hardness tests use different indenter materials and shapes Brinell Rockwell Vickers Knoop

FIGURE 2. 12 Selected hardness testers FIGURE 2.12 Selected hardness testers. (a) A Micro Vickers hardness tester; (b) Rockwell hardness tester; (c) Durometer; (d) Leeb tester. Source: (a) through (c) Courtesy of Newage Testing Instruments, Inc.; (d) Courtesy of Wilson® Instruments.

FIGURE 2.13 General characteristics of hardness-testing methods and formulas for calculating hardness.

Hardness and strength UTS=3.5(HB) SI units (UTS in MPa) UTS=500(HB) English units (UTS in psi) HB is Brinell hardness Since hardness is the resistance to permanent indentation it can be likened to performing a compression test on a small volume on the surface of a material

Fatigue Rapid fluctuating cyclic or periodic loads Parts fail at a stress level below that at which failure would occur under static loading Failure is found to be associated with cracks that grow with every stress cycle and propagate through the material FATIGUE FAILURE-responsible for the majority of failures in mechanical components Rotating machine elements under constant bending stresses as with shafts

Fatigue test Testing specimens under various states of stress, usually in a combination of tension and bending Stress amplitudes S Number of cycles N S-N Curves Endurance limit (fatigue limit): the maximum stress the material can be subjected without fatigue failure, regardless of N

FIGURE 2. 16 (a) Typical S–N curves for two metals FIGURE 2.16 (a) Typical S–N curves for two metals. Note that, unlike steel, aluminum does not have an endurance limit. (b) S–N curves for common polymers.

creep CREEP is the permanent elongation of a component under a static load maintained for a period of time. Metals, thermoplastics, rubbers Occurs at any temperature Recall: creep at elevated temperatures is attributed to grain- boundary sliding

Creep test The test generally consists of subjecting a specimen to a constant tensile load at elevated temperature and measuring the changes in length at various time increments Primary stage/Secondary stage/Tertiary stage STRESS RELAXATION-the stresses resulting from loading of a structural component decrease in magnitude over a period of time, even though the dimensions of the component remain constant (example: piano wire)

FIGURE 2.17 Ratio of endurance limit to tensile strength for various metals, as a function of tensile strength. Because aluminum does not have an endurance limit, the correlations for aluminum are based on a specific number of cycles, as is seen in Fig. 2.16.

FIGURE 2. 18 Schematic illustration of a typical creep curve FIGURE 2.18 Schematic illustration of a typical creep curve. The linear segment of the curve (secondary) is used in designing components for a specific creep life.

impact A typical impact test consists of placing a notched specimen in an impact tester and breaking the specimen with a swinging pendulum CHARPY IZOD Impact Toughness-the energy dissipated by breaking the specimen Materials with high impact resistance generally have high strength, ductility, toughness

FIGURE 2.19 Impact test specimens. (a) Izod; (b) Charpy.

Failure and fracture Fracture- through either internal or external cracking Ductile-plastic deformation which proceeds to failure Brittle–little or no gross plastic deformation Buckling – a long slender column under compressive loads

FIGURE 2.20 Schematic illustration of types of failures in materials: (a) necking and fracture of ductile materials; (b) buckling of ductile materials under a compressive load; (c) fracture of brittle materials in compression; (d) cracking on the barreled surface of ductile materials in compression.

FIGURE 2.21 Schematic illustration of the types of fracture in tension: (a) brittle fracture in polycrystalline metals; (b) shear fracture in ductile single crystals—see also Fig. 1.5a; (c) ductile cup-and-cone fracture in polycrystalline metals; (d) complete ductile fracture in polycrystalline metals, with 100%reduction of area.

FIGURE 2.23 Sequence of events in the necking and fracture of a tensile-test specimen: (a) early stage of necking; (b) small voids begin to form within the necked region; (c) voids coalesce, producing an internal crack; (d) the rest of the cross section begins to fail at the periphery, by shearing; (e) the final fracture, known as a cup- (top fracture surface) and-cone-(bottom surface) fracture, surfaces.

FIGURE 2.24 Schematic illustration of the deformation of soft and hard inclusions and of their effect on void formation in plastic deformation. Note that, because they do not conform to the overall deformation of the ductile matrix, hard inclusions can cause internal voids.

Transition temperature Many metals undergo a sharp change in ductility and toughness across a narrow temperature range Occurs mainly in bcc and hcp metals

FIGURE 2.25 Schematic illustration of transition temperature in metals.

Brittle fracture Occurs with little or no gross plastic deformation In tension fracture takes place along the crystallographic plane (cleavage plane) on which the normal tensile stress is a maximum In general low temperature & high deformation rate promote brittle fracture DEFECTS explain why brittle materials are weak in tension compared to compression CATASTROPHIC FAILURE-under tensile stresses cracks propagate rapidly

FIGURE 2.26 Fracture surface of steel that has failed in a brittle manner. The fracture path is transgranular (through the grains). Magnification: 200. Source: Courtesy of B.J. Schulze and S.L. Meiley and Packer Engineering Associates, Inc.

FIGURE 2. 27 Intergranular fracture, at two different magnifications FIGURE 2.27 Intergranular fracture, at two different magnifications. Grains and grain boundaries are clearly visible in this micrograph. The fracture path is along the grain boundaries. Magnification: left, 100; right, 500. Source: Courtesy of B.J. Schulze and S.L. Meiley and Packer Engineering Associates, Inc.

Residual stress Residual stresses are those that remain in a workpiece after it has been plastically deformed and then has had all external forces removed Eliminated by stress-relief annealing, further plastic deformation, or relaxation over time

FIGURE 2.30 Residual stresses developed in bending a beam having a rectangular cross section. Note that the horizontal forces and moments caused by residual stresses in the beam must be balanced internally. Because of nonuniform deformation, especially during coldmetalworking operations, most parts develop residual stresses.