MATERIALS SELECTION FOR SPECIFIC USE-1 Sub-topics 1 Density What determines density and stiffness? Material properties chart Design problems
LOADING 2
STRENGTH AND STIFFNESS Stress is applied to a material by loading it Strain a change of shape is its response Stiffness is the resistance to change shape that is elastic the material will return to its original shape when unloaded Strength is the resistance to permanent 3 distortion or total failure
MATERIAL PROPERTIES Stress and strain are not material properties they describe a stimulus and a response Stiffness and strength are material properties which are measured by the elastic modulus (E), elastic limit (σ y ), and tensile strength (σ ts ) Stiffness, strength, and density are three material properties central to mechanical design 4
HOW TO MEASURE MATERIAL DENSITY? Mass per unit volume kg/m 3 or lb/in 3 Double-weighing method for calculating density 5
MODES OF LOADING The elastic response depends on the way the loads are applied. (a) axial tension (b) compression (c) axial tension on one side and compression on the opposite side (d) torsion (shear) (e) bi-axial tension or compression 6
1 N/m 2 = 1 Pascal (Pa) 10 6 Pa = 1 MPa STRESS (a) Force applied normal to surface Positive F indicates tension Negative F indicates compression (b) Force applied parallel to surface Shaded plane carries the shear stress (c) Equally applied tensile and compressive forces on all six sides of a cubic element Hydrostatic pressure 7
STRESS-STRAIN CURVES Initial portion of curve is approximately linear and is elastic the material returns to its original shape once the stress is removed Within the linear elastic region, strain is proportional to stress E: Young s modulus G: shear modulus K: bulk modulus 8
STRAIN Strain is the ratio of two lengths and is therefore dimensionless Tensile stress lengthens the element causing a tensile strain (+) Compressive stress shortens the element causing a compressive strain (-) 9
POISSON S RATIO Negative of the ratio of transverse strain to axial strain in tensile loading Relates the Young s modulus, shear modulus, and bulk modulus to one another 10
MODULUS DENSITY CHART Identifies materials that are both stiff and light Critical for material selection of stiffness-limited designs 11
MATERIALS FOR STIFFNESS LIMITED DESIGN A cylindrical tie-rod loaded: (a) in tension, (b) in bending, (c) in torsion and (d) axially, as a column. The best choice of materials depends on the mode of loading and on the design goal. 12
LOADING CONDITIONS AND SHAPE 13
MATERIAL INDICES FOR ELASTIC DESIGN 14
ELASTIC EXTENSION OR COMPRESSION Relation between load, deflection and stiffness Shape of cross-section does not matter because the stress is uniform across the section 15
MINIMIZING WEIGHT A light, stiff tie-rod: Length, L o, is specified Design Requirements Must carry a tensile force F without extending elastically by more than δ Stiffness must be at least S* = F/δ Must have some toughness Objective is to make it as light as possible Cross-section area is free 16
DESIGN REQUIREMENTS 17
Objective function: equation that describes the quantity to be maximized or minimized The goal is to minimize the value of the objective function within the given constraints Constraint: Section area A must be sufficient to provide a stiffness of S* 18
MATERIAL INDEX (M T ) OF LIGHT, STIFF TIE-ROD It is most common to express material indices in a form for which a maximum value is sought High values of Mt are the best choice; the function E/ρ is called the specific stiffness 19
Ranking: indices on charts Selection lines are used based on the material indices All materials that lie on the selection line perform equally well; those that lie above the line perform better 20
METHOD FOR EARLY TECHNOLOGY SCREENING Design performance is determined by the combination of: CShape CMaterials CProcess Performance isn't just about materials - shape can also play an important role Shape can be optimized to maximize performance for a given loading condition Simple cross-sectional geometries are not always optimal Shape is limited by material Goal is to optimize both shape and material for a given loading condition do not underestimate impact of shape or the limitation of process 21
LOADING CONDITIONS AND SHAPE Different loading conditions are enhanced by maximizing different geometric properties 22
MINIMIZING WEIGHT OF BEAM Beams come in many shapes; Let s firstly consider beam of square cross-section 23
SHAPES AND MOMENTS 24