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Plasticity, Ductility. Yield strength is the stress beyond which a material becomes plastic – deformation is permanent Determined by standard tensile testing procedures Units: Mpa - MN/m 2 or psi - lb/in 2 1 Mpa = 145.05 psi. Figure 6.1.
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Yield strength is the stress beyond which a material becomes plastic – deformation is permanent • Determined by standard tensile testing procedures • Units: Mpa - MN/m2 or psi - lb/in2 • 1 Mpa = 145.05 psi
Figure 6.1 Yield strength σy is defined by a 0.2% offset from the linear elastic region When strained beyond σy, most metals work harden, causing the rising part of the curve Maximum stress is defined as the tensile strength σts
Figure 6.2 σy is identified as the stress at which the stress-strain curve becomes markedly non-linear, typically around a strain value of 1% The behavior of the polymer beyond the yield point depends on its temperature relative to the materials glass transition temperature
Figure 6.3 Glasses and ceramics have a yield strength; however, it is so large that it is never reached during a tensile test – the material fractures first The elastic limit σel is defined by the end of the elastic region of the stress-strain curve – this is the value generally used to compare the strength of ceramics with other materials
Figure 6.4 Tensile and compression tests require a large sample and are destructive – hardness tests require only a small volume and are non-destructive In a hardness test, a diamond or ball shaped indenter is pressed into the surface of a material The hardness of the material is determined by its resistance to the indentation
Figure 6.5 Most common are Brinell and Rockwell Units for hardness change based on which scale is used
Figure 6.8 Yield strain is the strain at which the material ceases to be linearly elastic – polymers have large yield strain (0.01 – 0.1) while the value for metals is at least a factor of 10 smaller
Figure 6.9 Stress – strain curve for a single atomic bond Ideally, the strength of a material is the force necessary to break inter-atomic bonds A bond is broken if it is stretched beyond about 10% of its original length – therefore the force needed to break a bond is roughly:
Figure 6.10 Further calculations that account for the curvature of the force-distance curve predict a ratio of 1/15
Figure 6.11 Defects in metals and ceramics prevent materials from achieving their ideal strength Common Defects: Vacancies Solute atoms on interstitial and substitutional sites Dislocations Grain boundaries
Vacancies A vacancy is a site at which an atom is missing – while vacancies play a role in diffusion, creep, and sintering, they do not influence strength Solute Atoms Substitutional solid solution – dissolved atoms replace those of the host Interstitial solid solution – dissolved atoms squeeze into spaces or “interstices” between the host atoms Dissolved atoms rarely have the same size as the host material, so the surrounding lattice is distorted
Dislocations A dislocation is an extra half-plane of atoms in the crystal – in the figure, the upper part of the crystal has one more double-layer of atoms than the lower part – dislocations distort the lattice and make metals soft and ductile Grain Boundaries Grain boundaries form when differently oriented crystals meet – the individual crystals are called grains, the meeting surfaces are grain boundaries
Figure 6.12 The edge dislocation is made by cutting, slipping, and rejoining bonds across a slip plane The dislocation line separates the part of the plane that has slipped from the part that has not (b) represents the resulting atomic configuration – called an edge dislocation because it is formed by the edge of the extra half-plan
Figure 6.13 When a dislocation moves it makes the material above the slip plane slide relative to that below • Initially perfect crystal (b) – (d) the passage of the dislocation across the slip plane shears the upper part of the crystal over the lower part by the slip vector b; when it leaves, the crystal has suffered a shear strain
Figure 6.14 In a screw dislocation, the upper part of the crystal is displaced parallel to the edge of the cut rather than normal to it All dislocation are either edge or screw or mixed, meaning they are made up of little steps of edge and screw In the screw dislocation, the slip vector b is parallel to the dislocation line S – S
Figure 6.15 For a dislocation to move, only bonds along the line it moves must be broken – this is significantly easier than breaking all of the bonds in the plane In crystals there are preferred planes and directions for which dislocation movement is easier – these are called the slip planes and slip directions Slip displacements are tiny – however, if a large number of dislocations travers a crystal, moving on many slip planes, the material deforms at a macroscopic level
Crystals resist the motion of dislocations with a friction-like resistance f per unit length Dislocations move from an applied shear stress τ – as they move the upper half of the crystal shifts relative to the lower half by a distance b Figure 6.16 Dislocations move if τ exceeds f/b
Figure 6.17 Drawing aligns polymer chains in the direction in which the material is stretched – this can increase strength and stiffness by a factor of 8 Polymers with high Tg cannot be drawn at room temperature – they craze, forming small crack-shaped regions within the polymer When crazing limits ductility in tension, large plastic strains may still be possible in compression by shear banding
Figure 6.18 The way to strengthen crystalline materials is to make it harder for dislocations to move
Two factors determine the influence of obstacles on dislocation movement: • Spacing • Strength L: distance between obstacle and the slip plane NL: number of obstacles touching unit length of dislocation line p: pinning force exerted by obstacle on dislocation line α: dimensionless constant characterizing the strength of obstacle The shear stress needed to force the dislocation through a field of obstacles
Strengthening of a metal by alloying – deliberate additions of impurities Alloying elements are generally bigger than those of the host material, making it harder for dislocations to move
Dispersion: disperse small, strong particles into a liquid metal, trapping the particles when it is cast in to shape Precipitation: solute dissolved in a metal while bother are molten; precipitates as small particles when cooled Dispersed and precipitated particles obstruct dislocation movement
Caused by the accumulation of dislocations generated by plastic deformation Dislocation density is defined as the length of dislocation line per unit volume
If a dislocation advances, it shears the material above the slip plane relative to that below, creating a little step called a jog Contribution of work hardening to the shear stress required to move the dislocation Pinning force exerted on dislocations by jogs
Figure 6.20 Successive positions of a dislocation as it bypasses particles that obstruct its motion.
Grain size D is typically 10-100 μm Dislocations cannot simply slide from one grain to the next because the slip planes do not line up Effect of grain boundaries on shear strength required for a dislocation to move
Approximation of shear yield strength based on strengthening mechanisms This describes the yield strength of a singled crystal loaded in shear – we need the yield strength of a polycrystalline material loaded in tension
Many engineering materials can be strengthened through various hardening mechanisms – however, an increase in strength almost always results in a decrease in ductility
Figure 6.22 The figure shows strengthening mechanisms and their effect on ductility – mechanisms are frequently combined, but an increase in strength will generally lower the ductility
Dislocations do not play a role in the strength of non-crystalline solids – instead, the relative slippage of two segments of a polymer chain must be considered Impeding the slippage of molecular chains can be done through blending, drawing, cross-linking, and by reinforcement with particles, fiber, and fabrics
Figure 6.23 Stronger alloys tend to have lower ductility
SUMMARY and CONCLUSIONS • Load Bearing Structures require materials with reliable, known strength. • There are several measures of strength • Elastic Design requires: • NO PART of the structure suffers plastic deformation • No stresses should exceed the yield strength • Plastic Design requires: • Some parts of the structure can deform plastically but the whole structure must survive. • Ductility and Tensile Strength become important properties • Materials can be made stronger • Metals, Ceramics: stopping dislocations from moving • Polymers: increasing bond strength between chains
