Lec 4 - Material properties


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LEARNING OBJECTIVES Understand the concept of material properties What do we mean by relationship of - with material properties What are the types of Engineering materials Examples of various properties

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Elastic Deformation, Failure – Single Stress States Axial Deformation Material testing Hook’s Law Strain Energy Thermal Strain Elastic deformation of materials will be the focus of this course. Plenty of challenging problems in this area…

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Elastic Behaviour of Materials - 2.1.1) Elastic Stiffness (Robert Hooke, 1648) Elastic deformation of materials will be the focus of this course. Plenty of challenging problems in this area… 2.1.2) Material Properties (Thomas Young, 1810) 2.2) Thermal Stress/Strain (William Rankine, 1870) 2.1.3) Mat. Props (Cont.) (Simon Poisson, 1825) As in all areas of science, a variety of people have made significant contributions to the Mechanics of Materials. The A-list: Simple Normal and Shear Loading

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Robert Hooke was the first to experiment with and define the stiffness of materials. Stiffness (Robert Hooke, 1648) “ Ut tensio sic vis” He suspended various masses from springs, and measured the extension.

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Elastic Behaviour K depends on: i) Material Properties ii) Geometry of Bar (i.e. L and A)

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Thomas Young helped to develop the theory of how materials deform elastically. In particular, he defined an important material constant, “Young’s Modulus”. Material Properties (Thomas Young, 1810)

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A variety of testing machine types, and sizes…

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Material samples are used in a variety of geometries… …and a number of techniques are used to accurately measure dimension changes.

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Young considered the load-extension behaviour of materials, converting this to stress-strain data. P P L0 u A0 Engineering stress and engineering strain are calculated as:

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The plot below illustrates both engineering stress and true stress plotted against strain, for a steel sample tested to destruction. Note: Very little difference between engineering and true values in elastic region.

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Young observed that the s-e slope was a constant for a particular material, independent of the sample geometry. He defined an important material parameter, now known as the modulus of elasticity, or Young’s modulus.

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Poisson made important observations and theories about lateral deflections of materials. Material Properties (Cont.) (Simon Poisson, 1825) When a bar is placed in tension, lateral contractions accompany the extension.

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This figure demonstrates the same concept, in tension and compression. Note: While we have lateral deformations, no loads have been applied in these directions.

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If we use Mild Steel: DL=0.24 mm, Dw=-0.00143 mm If we use Aluminum: DL=0.71 mm, Dw=-0.00471 mm If we use Nylon: DL=17.9 mm, Dw=-0.143 mm 0.015% increase in Volume 0.048% increase in Volume 0.64% increase in Volume

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Material Properties (so far…) We have now introduced three important material properties that govern the elastic behaviour of common engineering materials. They relate the stresses to the strains.

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The relationship between shear stress and shear strain can be explored through torsion of thin circular tubes. Shear Stress-Strain Diagram

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A useful relationship exists between E, n, and G. For typical engineering materials, the following relationship can be derived. If E and n can be obtained from a tensile test, G can be calculated from this relationship.


CONCLUSION We have studied : Engineering Materials Respective Properties Hooke’s Law Stress-Strain Diagram

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A Scottish engineer, Rankine made observations about the expansion and contraction of materials due to changes in temperature. Thermal Strains (William Rankine, 1870) a=Coefficient of Linear Expansion (A material property) He noted that these deflections were proportional to the change in temperature the material experienced.

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From Hooke’s Law: (Due to Forces and Temperature Changes)

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Castigliano related deformations due to forces applied to elastic bodies, to energy stored in that body (i.e. stored elastic potential energy). Strain Energy (Carlo Castigliano, 1881) Energy can be stored due to tension, compression, bending or torsion. Recall from Engineering Mechanics that energy stored in a spring during deformation is: For uniaxial stress, stored energy is the area under the P vs u graph.

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Material Failure In application, failure is defined by the physical situation… Is permanent deformation considered failure? Or, does fracture define failure? …AND the type of material. We compare stress applied to an object, to some limiting stress. Is only a finite amount of elastic deformation allowed?

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Concrete is a highly brittle material, having a much greater strength in compression (sc=34.5 MPa) than tension (st=2.76 MPa).

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Summary From considerations of equilibrium we establish the loads applied to a device. In a simple geometry, we have considered how internal forces are related to stress and some basic material properties relating stresses to strains. Load Carrying System STRENGTH (or Resistance to Failure)

Strength : 

Strength Measure of the material property to resist deformation and to maintain its shape It is quantified in terms of yield stress or ultimate tensile strength. High carbon steels and metal alloys have higher strength than pure metals. Ceramic also exhibit high strength characteristics.

Hardness : 

Hardness Measure of the material property to resist indentation, abrasion and wear. It is quantified by hardness scale such as Rockwell, Vickers and Brinell hardness scale. Hardness and Strength correlate well because both properties are related to in-molecular bonding.

Hardness Testing Techniques : 

Hardness Testing Techniques

Relationship between hardness and strength : 

Relationship between hardness and strength

Ductility : 

Ductility Measure of the material property to deform before failure. It is quantified by reading the value of strain at the fracture point on the stress strain curve. Example of ductile material : low carbon steel Aluminum It may be expressed by either

Ductility (contd) : 

Ductility (contd)

Brittleness : 

Brittleness Measure of the material’s inability to deform before failure. The opposite of ductility. Example of brittle material glass, high carbon steel, Ceramics

Toughness : 

Toughness The ability of a metal to deform plastically and to absorb energy in the process before fracture is termed toughness. Toughness is the area under the stress-strain curve, and is a measure of the total energy absorbed until failure. There are several variables that have a profound influence on the toughness of a material. These variables are: Strain rate (rate of loading) Temperature Notch Effect

Toughness (contd) : 

Toughness (contd) A metal may possess satisfactory toughness under static loads but may fail under dynamic loads or impact. As a rule ductility and, therefore, toughness decrease as the rate of loading increases. Temperature is the second variable to have a major influence on its toughness. As temperature is lowered, the ductility and toughness also decrease. The third variable is termed notch effect, this is mainly related to the distribution of stress. A material might display good toughness when the applied stress is uniaxial; but when a multiaxial stress state is produced due to the presence of a notch, the material might not withstand the simultaneous elastic and plastic deformation in the various directions.

Toughness (contd) : 

Toughness (contd) Impact toughness can be measured by Charpy V-Notch Test The potential energy of the pendulum before and after impact can be calculated form the initial and final location of the pendulum. The potential energy difference is the energy it took to break the material.  absorbed during the impact. At low temperature, where the material is brittle and not strong, little energy is required to fracture the material. At high temperature, where the material is more ductile and stronger, greater energy is required to fracture the material The transition temperature is the boundary between brittle and ductile behavior. The transition temperature is an extremely important parameter in material selection.



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NUMERICAL Determine the equivalent distributed loads and support reactions for the simply supported beam which is subjected to given distributed loads. SF & BM 41



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INTRODUCTION TO BEAMS AND FLEXULAR LOADS Beams - structural members supporting loads at various points along the member Objective - Analysis and design of beams Transverse loadings of beams are classified as concentrated loads or distributed loads Applied loads result in internal forces consisting of a shear force (from the shear stress distribution) and a bending couple (from the normal stress distribution) 43

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