Mechanical properties of materials

Transcription

1 Mechanical properties of materials The behavior of material is mainly determined by various mechanical properties of the material when subjected to different loading conditions. Such properties mainly include Young s modulus, various types of strength of the material, hardness, ductility etc. and are found to be very important both for design & manufacturing viewpoint. The design engineer should also consider the manufacturing constraints during the design of a part. Three basic types of stresses which are produced when a material is subjected to various loading conditions are a) Tensile Stress b) Compressive Stress c) Shear stress Tensile properties Tensile strength is defined as the ability of a material to support axial load without rupture and is determined through the tensile test. When equal and opposite forces are applied simultaneously at both the ends that pulls the material, it tries to elongate it and the diameter reduces. The test specimen and general setup has been shown in the Figure M (a)

2 (b) Figure M1.4.1: (a) Test specimen (b) Setup for the test Due to the stretching of the specimen in tensile test, the initial test specimen length L0 is increased to L and area A0 is reduced to A. The tensile testis carried out at a constant cross head speed and extensometers of required gauge length are used to capture the elongation depending on the requirement. In this process the material first elongates, then necking occurs & the fracture is produced. The necking phenomenon is observed mostly in tensile test and it also mainly depends upon the material that isused for test. If the material is brittle there is no chance of necking. From the measured data from the tensile test, the stress- strain curve is plotted. Mainly there are two type of stress-strain curves which are described below: 1) Engineering stress-strain 2) True stress strain

3 Generally in design application the engineering stress-strain curve is used as there is no expectation of change in shape due to strain. The true stress strain curve is important in manufacturing. Engineering stress-strain Engineering stress-strain is mainly illustrated by taking original cross section and original length. The stress-strain diagram for a metal is shown in Figure M Figure M1.4.2: Engineering stress-strain diagram of an metal The engineering stress at any point on the curve is the force divided by the original area s = F A Where e= Engineering stress (MPa) F= applied force in the test, (N) Ao= Original area of the test specimen (mm 2 ) Engineering strain at any point is the ratio between change in length to the original gage length.

4 e = L L L Where e= engineering strain, mm/mm, L= length at any point during elongation, mm Lo= Original gage length, mm Further, in the stress-strain curve, two distinct regions namely elastic region and plastic region represent different material behavior of the material. In the elastic region, the relation between stress and strain is linear. The relationship between stress and strain in the elastic region is defined by Hooke s law: s = Ee Where E= Young s modulus, MPa The value of E varies form one material to other which mainly indicates the stiffness of the material. In further addition of stress, the material begins to yield which is the end point of the elastic region (shown in the Figure M1.4.2). At this point there is change in slope of the curve occurs. This point is called as yield point which could be measured by drawing a straight-line parallel to the slope of the load-extension curve of the metals like titanium, steel, low carbon steel, and molybdenum at 0.2% offset. At this yield point there is slight extension of the specimen occurs without increase in stress level. The strength of the material at this point is called as yield strength. Beyond yield point, as the load increases, elongation of the specimen proceeds at a faster rate than before. This part of stress strain curve is called hardening region.when the load reaches a maximum value, the engineering stress at this point is called the tensile strength or ultimate tensile strength of the material. In the stress- strain diagram, beyond the tensile strength, the load carrying capacity reduces and the test specimen goes through a localized elongation called necking.there will not be constant strain in this region and the elongation occurs in one small segment of the specimen. The stress measured just before failure is known as the fracture stress.

5 The amount of strain that the material sustain before failure is an important property in mechanical engineering, which is used specially in manufacturing. This property is called ductility and is measured in terms of elongation or area reduction. EL = L L L AR = A A A Where EL= elongation, in % Lf= Specimen length in mm Lo= Original specimen, mm AR= Area reduction, in % Ao= Original area, mm 2 Af=Area of cross-section at the point of facture, in mm 2 True Stress-strain In the computation of engineering stress, the original cross sectional area has been used. However, during the process of loading the area reduces. In the computation of true stress the actual or instantaneous area is used. As the length increases, the cross sectional area decreases. Hence the calculated stress value will be higher. The instantaneous load divided by instantaneous cross-sectional area is called true stress. σ = F A Where = true stress, MPa F= force, N A=Actual area resisting the load, mm 2 True Stress & strain is related to engineering stress & strain in the following way. Keeping the volume of material constant.

6 A L = A L = F A = F A A A = s L L = s L L + L L = s (1 + e) Similarly true strain offers a more accurate calculation of the instantaneous elongation per unit length of the material.the true stress is generally increased rapidly than engineering stress once the strain increases and the accordingly, the cross sectional of the specimen decreases. ϵ = dl L = ln L L = ln L L + L L = ln (1 + e) Where L= instantaneous length at any moment during elongation ϵ = true strain The true stress-strain relationship in plastic region can be represented by the following flow curve: σ = K Here the constant K=strength coefficient n= Strain hardening exponent The value of K & n varies form one metal to other & mainly depends upon metal s tendency to work harden. The behavior of nearly all type of solid material are described by three types of stress-strain relationship diagram as shown in Figure M A) Perfectly elastic The behavior of the material is absolutely defined by its stiffness. Such material directly fractures without yielding when it reaches ultimate strength material. These materials are called

7 brittle materials. Examples of brittle material are ceramics, cast iron, etc. These materials are not suitable for forming operation, where permanent plastic deformation is required to get the final product. B) Elastic and perfectly plastic For this type of material, when the stress level reaches the yield point plastic deformation begins at the same stress level. Metals behave in this mode, when they are heated to high temperatures. This type of behavior occurs mainly at higher temperature doesn t strain harden rather it recrystallize during deformation. C) Elastic and strain hardening This kind of material obeys Hooke s law in the elastic region and begins to flow at its yield point. During cold working, most of the ductile material behave in this manner. Figure M1.4.3: The stress-strain relationship diagram for a) perfectly elastic b) elastic & perfectly plastic c) elastic & strain hardening. Compression Properties Compressive test is performed to determine the compressive strength of the material. The material is applied equal and opposite compressive load. Engineering stress is defined as s = F A Where Ao= Original area of cross section, mm 2 Engineering strain is defined as

8 = h h h Where h= height of the specimen at a particular moment into the test, mm h0= starting height, mm The strain will be negative. Usually the negative sign of the strain are ignored. The stress strain diagram is shown in the Figure M The stress strain curve shown in Figure M1.4.4 for compression test is different in the plastic region of stress strain curve for tensile test for same material. The reason of this variation is compression helps in increase in the cross section. The load rises more quickly than the tensile test. In compression operation, due to friction between the surfaces there is an increase in area of the middle of the specimen than at the ends. This effect is called barreling effect in a compression test. Figure M1.4.4: Stress-strain diagram for compression test Compression operations are used mostly in metal forming than stretching operations. Generally forging, rolling etc. are the compression operation used in industry.

9 Shear properties Shear stress involves application of load parallel to the surface of material in opposite direction as shown in Figure M The shear stress is defined as τ = F A (a) (b) Figure M1.4.5: Shear (a) stress (b) strain Where τ = shear stress, MPa F= applied force, N A= area over which the force is applied, mm 2 Shear strain can be defined as γ = δ b Where γ =shear strain, mm/mm δ= the deflection of the element, mm b= the orthogonal distance over which deflection occurs, mm In case of shear stress strain curve, the relationship for elastic region is defined by

10 = Where G=the shear modulus, MPa For plastic region the relationship between the shear stress strain is similar to flow curve. Due to strain hardening the applied load increases until the fracture occurs. The relationship between shear strength (S) & Tensile strength (TS) can represented by data approximation as below: S = 0.7 (TS) Different cutting operations like blanking, punching etc. used in industry are included in shearing operation. Due to mechanism of shear deformation the material is removed in the machining process. Hardness Hardness is a measure of how resistant solid matter is to various kinds of permanent shape change when a force is applied. Vickers hardness test: It is easier to use in comparison to other hardness tests since the required calculations are independent of the size of the indenter, and the indenter can be used for all materials irrespective of hardness. The unit of hardness given by the test is known as the Vickers Pyramid Number (HV). In Vickers hardness test the surface is subjected to a standard pressure for a standard length of time by means of a pyramid-shaped diamond. The diagonal of the resulting indention is measured under a microscope and the Vickers Hardness value is read from a conversion table. The Vickers number (HV) is calculated as: HV = 1.854(F/D 2 ) Where F=the applied load,kgf D= the area of the indentation, mm 2

11 Brinell hardness test:it is widely used for testing metals and non-metals of low to medium hardness. A ball shaped indenter made of cemented carbide is used for harder material in this test. Knoop Hardness Test: It is used for generally small & thin specimen. A pyramid-shaped diamond indenter is used whose length-to-width ratio of about 7:1. Rockwell Hardness Test: It is used for variety of material like carbide, ceramic, tool steel etc. where a cone-shaped indenter, with diameter 3.2 mm is forced into the specimen using a minor load of 10 kg & then a major load of 150 kg is applied, helping the indenter to penetrate into the specimen a certain distance beyond its initial position. This extra penetration distanced is converted into a Rockwell hardness. There is a good correlation between hardness & strength for most metals as hardness is usually based on resistance to indentation, which is a form of compression. Brinell hardness (HB) shows a close correlation with the ultimate tensile strength (TS) for steel is given below: TS = 3.45 (HB)