Dobson+CH7 - MECHANICAL PROPERTIES When a material is...

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Unformatted text preview: MECHANICAL PROPERTIES When a material is employed in a specific application, will it be subjected to high stress, elevated stress, stress at high or low temperatures, cyclic stress, corrosive or abrasive environments? The focus is to understand how a material will respond to such stress, and ensure that failure will not result in the intended application. MECHANICAL PROPERTIES • Stress and strain: What are they and why are they used instead of load and deformation? • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? Stress and Strain: Concepts Stress is defined as the force acting on the unit area over which the force is applied. Stress has units of force/area (i.e. psi, Pascals, N/m2). Strain is defined as the change in dimension per unit length. Strain is effectively dimensionless, yet is reported in units such as in./in. Stress and Strain: Concepts • Simple Tension: Cable F F A o = cross sectional area (when unloaded) Ski lift (photo courtesy P.M. Anderson) σ = F Ao σ σ Stress = Force per unit Area Stress and Strain: Concepts One of the most common materials tests is the tensile test, in which a specifically shaped sample is placed under an increasing tensile load (force). The physical deformation of the sample is measured as a function of applied force. Stress and Strain: Concepts To account for differences in sample specimen sizes, the results of tensile tests are reported as engineering stress (σ). This stress is still defined as the force acting on an area, but now the specific area is used to calculate the stress. F σ= A0 Likewise, engineering strain (ε) is defined as the change in specific dimensions of the sample. per unit length. In the expression below, li is the instantaneous length and l0 is the initial length. li − l0 Δl ε= = l0 l0 6-5 Stress and Strain: Concepts • Simple Compression: Ao Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) σ = F Ao Stress and Strain: Concepts Shear and Torsional tests: •  Shear test: a load of force (F) is imposed on the specimen parallel to the upper and lower faces. •  Shear: The ratio of force (F) per area is used to define shear stress (τ) τ= F A0 •  Shear strain (γ) is defined as the tangent of the strain angle θ. •  Torsional test: variation of shear, rotational motion about the longitudinal axis •  Torsional shear stress is a function of applied torque (Τ) •  Torsional shear strain is related to the angle of twist φ. Stress and Strain: Concepts Geometric Considerations •  Stress state is a function of the orientation of the planes upon which the stresses are taken to act •  Stress on plane p-p’ is no longer purely tensile •  Plane p-p’ has both normal tensile stress (σ’) that acts perpendicular to the plane and shear stress (τ’) that acts parallel to the plane ⎛ྎ 1 + cos 2θ ⎞ྏ σ ʹȃ = σ cos θ = σ ⎜ྎ ⎟ྏ 2 ⎝ྎ ⎠ྏ 2 ⎛ྎ sin 2θ ⎞ྏ τ ʹȃ = σ sin θ cosθ = σ ⎜ྎ ⎟ྏ ⎝ྎ 2 ⎠ྏ Stress and Strain: Concepts TENSILE STRESS COMPRESSIVE STRESS SHEAR STRESS TORSIONAL STRESS Stress and Strain: Behavior •  When the strain experienced under stress is reversible, it is referred to as elastic strain. •  Deformation in which stress and strain are proportional is called elastic deformation. •  The relationship between stress and strain, reflected in a stress-strain curve, is characteristic of specific materials and is expressed as the modulus of elasticity. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Stress and Strain: Behavior •  The slope of the stress-strain curve is defined as the Young’s modulus (E) of a material. •  If the stress strain response is nonlinear, the tangent or secant modulus of elasticity (E) is used. •  The relationship between stress (σ) and strain (ε): σ = Eε Copyright © 2006 by Nelson, a division of Thomson Canada Limited E L 1 Stress and Strain: Behavior When a material is subjected to a tensile load, the elongaFon that occurs is accompanied by a respecFve lateral constricFon, due to the conservaFon of volume. This property is captured by Poisson’s ra*o (v). Δl ε= l0 εy εx ν =− =− εz εz Copyright © 2006 by Nelson, a division of Thomson Canada Limited Stress and Strain: Behavior •  Relationships between tensile stress and strain exist for conditions of shear. •  Shear stress (τ) and shear strain (γ) are proportional to each other thorough the shear modulus (G). τ = Gγ •  For isotropic materials, the shear modulus is related to the Young’s modulus through Poisson’s ratio according to the relationship: E = 2G(1 +ν ) Copyright © 2006 by Nelson, a division of Thomson Canada Limited Stress and Strain: Behavior Modulus values: •  Material specific •  Temperature dependent •  Related to atomic bonding Copyright © 2006 by Nelson, a division of Thomson Canada Limited PlasFc DeformaFon Materials that exhibit large nonlinearities in their stress-strain properties are referred to as elastomers. Metals typically exhibit elastic behavior to ~0.005 strain. Materials which do not exhibit reversible stress-strain behavior are said to experience plastic strain or to undergo plastic deformation. The process of transitioning to plastic behavior is known as yielding. The point at which irreversible behavior is detected is known as the proportional limit (P). If a discreet transition is observed, it is called the yield point. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Tensile ProperFes The proportional limit is often hard to observe reproducibly. As a result, the onset of plasticity is defined by constructing a line parallel to the elastic portion of the curve at a point of 0.002 strain. The intersection with the stressstrain curve is defined as the yield strength (σy). Copyright © 2006 by Nelson, a division of Thomson Canada Limited Tensile ProperFes Materials exhibiting a yield point behavior often exhibit repeated yielding stress below the initial yield point. The yield strength in this case is taken as the stress corresponding to the lower yield point. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Tensile ProperFes Metals subjected to conFnued stress will exhibit a maximum (M) in the stress- strain curve. The value of the stress at this point is defined as the tensile strength. ConFnued applicaFon of stress ulFmately results in fracture (F). www.youtube.com/watch?v=W5A8gU37wGg&feature=related Copyright © 2006 by Nelson, a division of Thomson Canada Limited Tensile ProperFes Duc*lity is defined as the degree of plasFc behavior exhibited before fracture (failure). Materials exhibiFng liRle plasFc behavior are said to be bri*le. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Tensile ProperFes Duc*lity can be quanFfied by either percent elonga2on (%EL) or percent reduc2on in area (%RA). (l (%EL ) = f − l0 ) l0 × 100 (A − A ) ×100 (%RA) = 0 f A0 Copyright © 2006 by Nelson, a division of Thomson Canada Limited True Stress & True Strain PlasFc deformaFon beyond the tensile strength, might imply a weakening of the material- however it is actually ge9ng stronger. Insight into the behavior is gained by realizing that beyond this point the cross- sec2onal area is being reduced. To account for this, true stress (σT) and true strain (εT) values are reported under these condiFons. F σT = Ai li ε T = ln l0 Up to the point of necking, stress and true stress values (and likewise strain) are related by the equaFons: σ T = σ (1 + ε ) εT = ln(1 + ε ) Copyright © 2006 by Nelson, a division of Thomson Canada Limited ElasFc Strain Recovery As discussed previously, sequenFal stress- loading will result in a change in mechanical properFes. Note below changes in both strain (dimensional change) and yield strength as a funcFon of cycle. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Hardness Hardness is defined as a material’s resistance to localized plasFc deformaFon. This property is very dependent on the local geometry. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Hardness Hardness measurements are made as a funcFon of load, and indenter size and shape. These measurements entail the “visual” inspecFon of the size of the indent followed by the characterizaFon of hardness on a relaFve scale. Copyright © 2006 by Nelson, a division of Thomson Canada Limited 6-24 Hardness Hardness measurements are very common as they- • Are easy to perform • Are essenFally nondestrucFve • Can be related to other mechanical properFes. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Variability of Material ProperFes The measurement of mechanical properFes rouFnely produces a variaFon in measured values (see a). Such variaFon can result from • Instrumental error • User error • Sample inhomgeneity • Changes in environment n ∑x i x= i =1 #n n % ∑ xi − x SD = % i=1 % n −1 % $ ( 1/ 2 ) 2& ( ( ( ( ' Care must be exercised in reporFng values, employing averages (mean) and standard deviaFons, to accurately reflect the material and its property. Copyright © 2006 by Nelson, a division of Thomson Canada Limited Design Safety Factors Due to inherent uncertainFes in materials properFes, applicaFons are o^en designed (engineered) with significant margins of safety. For example, a safe stress or working stress (σw) may be used in design, incorporaFng a factor of safety, N . σw = σy N Values for N usually range from 1.2 to 4.0 and are dependent on many factors – e.g. economics, previous experience, measurement accuracy, consequences of failure… Copyright © 2006 by Nelson, a division of Thomson Canada Limited Stress and Strain Repeated, cyclical stress results in metal faFgue – progressive, localized structural damage. Stress and Strain SomeFmes the consequences of metal faFgue are relaFvely minor... Stress and Strain … and someFmes they’re not. Summary IllustraFon Copyright © 2006 by Nelson, a division of Thomson Canada Limited Foreshadowing discussion of materials classes Copyright © 2006 by Nelson, a division of Thomson Canada Limited ...
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