UNIT II MECHANICAL BEHAVIOUR OF STRUCTURES Mechanical Behaviour
UNIT II MECHANICAL BEHAVIOUR OF STRUCTURES Mechanical Behaviour: Stress-strain diagram showing ductile and brittle behaviour of materials, linear and non linear elastic behaviour and properties, mechanical properties in plastic range, yield strength offset yield strength, ductility, ultimate tensile strength, toughness. Plastic deformation of single crystal by slip and twinning.
Stress strain curve
Due to collective motion of many dislocations Yield point e UTS e → Elastic region Elastic + Plastic region X → → s → in a r t S d har g nin → Usually expressed as (for plastic) Fracture UTS- Ultimate Tensile Strength
Elastic behaviour ØWhen a solid material is subjected to external load, up to certain limiting loads the same solid will recover its original dimensions when the load is removed. The recovery of the original dimensions of a deformed body when the load is removed is known as “elastic behaviour”. (stress and strain are proportional) The limiting load beyond which material no longer behaves elastically is the “elastic limit”
Hooke’s law For most materials, as long as the load doesn’t exceed the elastic limit, the deformation is proportional to the load. This relationship is known as Hooke’s law; it is more frequently stated as “stress is proportional to strain ” Elastic deformations in metals are quite small and require very sensitive instruments for their measurement The inverse of Young’s modulus is known as the compliance of the material (or) The inverse of stiffness is compliance, typically measured in units of metres per newton
Linear elastic properties When stress is proportional to strain, elastic region shows the mechanical properties called: 1. stiffness 2. elastic strength 3. resilience A material with high value of modulus of elasticity is said to be stiff and a material with low value of modulus of elasticity is said to be resilient
Stiffness: deformation of a material is defined as its ability to resist the elastic Materials having high stiffness show less elastic deformation under load Modulus of elasticity is the measure of stiffness of a material Elastic strength: is a highest stress at which the behaviour of the material remains elastic Resilience: is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered As a material is deformed by an external loading, it tends to store energy internally throughout its volume. Since this energy is related to the strains in the material, it is referred to as strain energy.
It indicates the strain-energy density of the material just before it fractures. This property becomes important when designing members that may be accidentally overloaded. Alloying metals can also change their resilience and toughness. For example, by changing the percentage of carbon in steel, the resulting stress–strain diagrams in Fig (next slide) show the degrees of resilience and toughness can be changed
Schematic representations of tensile stress–strain behaviour for brittle and ductile metals loaded to fracture.
Non-linear elastic properties When stress is not directly proportional to strain, the curve is nonlinear The properties identified in this region are: Secant modulus and Tangent modulus is taken as the slope of the stress–strain curve at some specified level of stress, whereas secant modulus represents the slope of a secant drawn from the origin to some given point of the curve
Plastic behaviour If the elastic limit is exceeded, the body will experience a permanent set or deformation when the load is removed. A body which is permanently deformed is said to have undergone “plastic deformation” Stress-strain curve for M. S
Plastic flow in single crystals F Outward normal • Consider a single crystal subjected to a uniaxial tension as shown in Figure. As Slip direction Slip plane A o • At room temperature the major source for plastic deformation is the dislocation motion through the crystal lattice. • Dislocation motion occurs on fixed crystal planes (“slip planes”) in fixed crystallographic directions (corresponding to the Burgers vector of the dislocation that carries the slip). • The crystal structure of metals is not altered by the plastic flow.
Plastic flow in single crystals F Outward normal Slip direction As Slip plane Ao where, 1/m = Schmid – Boas factor
Plastic flow in single crystals • Plastic flow initiates when the resolved shear stress reaches a critical value: F Outward normal Slip direction As Slip plane Ao • where, CRSS is the critical resolved shear stress, and Y is the yield stress of the material. • The value of CRSS depends on temperature, strain rate, initial dislocation density and purity. The maximum τR is when φ = λ = 45 o. Or τCRSS = 0 when φ = 0 or λ = 0.
Macroscopic slip in a single crystal
Deformation by twinning Twinning occurs as atoms on one side of the boundary (plane) are located in mirror image positions of the atoms on the other side. The boundary is called twinning boundary. Twin results from atomic displacements produced from; 1) Applied mechanical shear force (mechanical twin) : in BCC, HCP 2) During annealing heat treatment (annealing twin) : in FCC. Note: twinning normally occurs when slip systems are restricted or when the twinning stress > critical resolved shear stress.
Deformation by slip Deformation by twinning
Characteristics of twinning Appears as broad lines or bands Planes of atoms move fractional distances Requires higher shear stress Occurs in metals having less number of slip systems
Engineering Stress (s) and Strain (e)
Comparison between “Engineering” and “True” quantities Strain • Stress
A comparison of typical tensile engineering stress–strain and true stress–strain behaviours
Proof stress The equivalent of yield stress in materials which have no clearly defined yield point Commonly the stress to produce 0. 2% extension is quoted in N/mm 2 for steel. This value approximates to the yield stress in materials not exhibiting a definite yield point Each inch of chart on the X-axis represents 0. 2% (0. 002 in. /in. ) of specimen elongation or extension
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