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# THE STRESS- STRAIN CURVE

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The Stress-Strain Curve A typical stress-strain curve is shown in Figure 2. This stress-strain curve is typical for ductile metallic clements. When a material reaches its ultimate stress strength of the stress- strain curve, its cross-sectional area reduces dramatically, a term known as necking. The “true” stress-strain curve could be constructed directly by installing a “gauge,” which measures the change in the cross sectional area of the specimen throughout the experiment. matetene stream Fracture streng Fracture 1 Yieldseth Nedang Young’s message Fracture Strain Pasta Figure 2. Various regions and points on the stress-strain curve and Theoretically, even without measuring the cross-sectional area of the specimen during the tensile experiment, the “true” stress-strain curve could still be constructed by assuming that the volume of the material stays the same. Using this concept, both the true stress (6), the true strain (er) could be calculated using Equations 3 and 4. respectively. In these equations L’ refers to the initial length of the specimen, I refers to the instantaneous length and refers to the instantaneous stress. 00- L (Equation 3) 3
= In (Equation 4) Figure I also shows that a stress-strain curve is divided into four regions: elastic, yielding. strain hardening (commonly occurs in metallic materials), and necking. The area under the curve represents the amount of energy needed to accomplish each of these events.” The total area under the curve (up to the point of fracture) is also known as the modulus of toughness. This represents the amount of energy needed to break the sample, which could be compared to the impact energy of the sample, determined from impact tests. The area under the linear region of the curve is known as the modulus of resilience. This represents the minimum amount of energy needed to deform the sample. The linear region of the curve of Figure 2. which is called the elastic region (past this region, is called the plastic region), is the region where a material behaves elastically. The material will return to its original shape when a force is released while the material is in its clastic region. The slope of the curve, which can be calculated using Equation 5, is a constant and is an intrinsic property of a material known as the elastic modulus, E. In metric units, it is usually expressed in Pascals (Pa). Young’s modulus, E During elastic deformation, the engineering stress-strain relationship follows the Hook’s Law and the slope of the curve indicates the Young’s modulus (E). Elastic Modulus, (E) Stressco) (Equation 5) Strain (E) Elastic Modulus, (E)=Slope of the graph (Equation 6) Young’s modulus is of importance where deflection of materials is critical for the required engineering applications. This is for examples: dellection in structural beams is considered to be crucial for the design in engineering components or structures such as bridges, building, ships, etc.
Yield strength, By considering the stress-strain curve beyond the elastic portion, if the tensile loading continues, yielding occurs at the beginning of plastic deformation The yield stress, can be obtained by dividing the load at yielding by the original cross-sectional area of the specimen (9) as shown in Equatica 7 “Yield Load (P2 Yield Strength (G)- Original Area (4) (Equation 7) true fracture stress 0 ultimate stress fracture stress proportional limiy elastic limit yield stress Oy Opl elastic yielding strain necking region hardening elastic plastic behavior behavior Figure 3. Strain-Strain diagram for ductile material (steel) The yield point can be observed directly from the load extension curve of the BCC metals such as iron and steel or in polycrystalline titanium and molybdenum, and especially low carbon steels, see Figure 3. The yield point clongation phenomenon shows the upper yield point followed by a sudden reduction in the stress or load till reaching the lower yield point. At the yield point elongation, the specimen continues to extend without a significant change in the stress level. Load increment is then followed with increasing strain. This 5
yield point phenomenon is associated with a small amount of interstitial or substitutional atoms. This is for example in the case of low-carbon steels, which have small atoms of carbon and nitrogen present as impurities. When the dislocations are pinned by these solute atoms, the stress is raised in order to overcome the breakaway stress required for the pulling of dislocation line from the solute atoms. This dislocation pinning is related to the upper yield point as indicated in Figure 4 (a). If the dislocation line is free from the solute atoms, the stress required to move the dislocations then suddenly drops, which is associated with the lower yield point. Furthermore, it was found that the degree of the yield point effect is affected by the amounts of the solute atoms and is also influenced by the interaction energy between the solute atoms and the dislocations. Aluminium on the other hand having a FCC crystal structure does not show the definite yield point in comparison to those of the BCC structure materials, but shows a smooth engineering stress strain curve. The yield strength therefore has to be calculated from the load at 0.2% strain divided by the original cross-sectional area as follows Yield Strength (o Yield Load (PX) Original Area (A) (Equation 8) The determination of the yield strength at 0.2% offset or 0.2% strain can be carried out by drawing a straight line parallel to the slope of the stress-strain curve in the linear section, having an intersection on the x-axis at a strain equal to 0,002 as illustrated in Figure 4 (b). An interception between the 0.2% offset line and the stress-strain curve represents the yield strength at 0.2% offset or 0.2% strain However offset at different values can also be made depending on specific uses: for instance, at 0.1 or 0.5% offset. The yield strength of soft materials exhibiting no linear portion to their stress-strain curve such as soft copper or gray cast iron can be defined as the stress at the corresponding total strain. It should be noted that the yield strength value can also be replaced by the ultimate tensile strength, for engineering designs
Stress Low Carbon Steel Yield point Localyield you Pure Alminium 300 TM Strain (a) 200 DAN -02 on 000 000 000 0010 (b) Figure 4. a) Comparative stress-strain relationships of low carbon steel and aluminium alloy and b) the determination of the yield strength at 0.2% offset. (stress) 0, B-025 offset yield strength stress E strain -0.2% offset o (strain, in in) & 0.002 in in 7
Ultimate Tensile Strength, or Beyond yielding, continuous loading leads to an increase in the stress required to permanently deform the specimen as shown in the engineering stress-strain curve. At this stage, the specimen is strain hardened or work hardened. The degree of strain hardening depends on the nature of the deformed materials, crystal structure and chemical composition, which affects the dislocation motion. FCC structure materials having a high number of operating slip systems can easily slip and create a high density of dislocations Tangling of these dislocations requires higher stress to uniformly and plastically deform the specimen, therefore resulting in strain hardening If the load is continuously applied, the stress-strain curve will reach the maximum point, which is the ultimate tensile strength (UTS, Ors). At this point, the specimen can withstand the highest stress before necking takes place. This can be observed by a local reduction in the cross-sectional area of the specimen generally observed in the centre of the gauge length Maximum Tensile Load Ultimate Strength = Original Area (1) (Equation 9) Fracture Strength, of After necking, plastic deformation is not uniform and the stress decreases accordingly until fracture. The fracture strength (Gators) can be calculated from the load at fracture divided by the original cross-sectional area, A, as expressed in Equation 10. (Equation 10) Tensile ductility Tensile ductility of the specimen can be represented as % elongation or % reduction in area as expressed in the equations given below
Strain, (E)= Change in Length (AL) Final Gauge Length – Inital Gauge Length Guage Length (L) Initial Gauge Length Elongation=x100 (Equation 11) Percentage of Reduction of Area – Change in Area (14)_ Original Area – Area at the breakage Original Area (A) Original Area 44 x100 (Equation 12) 4. A *100 = Where is the cross-sectional area of specimen at fracture. Limir of proportionality The limit of proportionality is the point beyond which Hooke’s law is no longer true when stretching a material. The elastic limit is the point beyond which the material you are stretching becomes permanently stretched so that the material does not return to its original length when the force is removed Load at limit of proportionality Limit of Proportion Original Area (A) (Equation 13) S EXPERIMENTAL PROCEDURE: 1. The load pointer is set at zero by adjusting the initial the initial setting mode. 2. Measure the dimensions of the test piece with the help of a Vernier caliper. Also mark the gauge length. 3. Now the specimen is gripped between the upper and middle crosshead jaws of the machine 4. Start the machine and the specimen is gradually loaded. Obtain the Stress-Strain graph and the corresponding results from the control interface control and analyze the results 5. Remove the broken specimen from the jaws safely, measure the dimensions again by keeping the broken specimen together, and tabulate them. 9
6. OBSERVATIONS: Ng Description Specimen (Mild Steel) 780 1 2 3 6.16 12.57 77.43 4 5 6 Initial Length (mm) Initial Gauge Length (mm) Initial Thickness (mm) Initial Width (mm) Initial Area (mm) – Width X Thickness Final Length after breaking (mm) Final Gauge Length after breaking (mm) Final Thickness (mm) Final Width (mm) Final Area at the breaking place (mm) Maximum Load after the specimen breaks (N) (From Stress-Strain Graph) 7 8 83-22 4.54 9.29 42.13 9 10 11 ZARESULTS: Specimen (Mild Steel) No. Description 1 2 3 4 5 6 6.66667 45.52) Young’s Modulus (GPa) Load at yield Point (N) Yield Strength (MPa) Ultimate Tensile Strength (MPa) % Elongation % Reduction in Area Limit of Proportionality Fracture Strain Work hardening exponent (n) Fracture mode Fracture surfaces (Sketches) 7 8 9 10 11 10
EXPERIMENT REPORT FORMAT AND GUIDE The general format of the project report is given as below. 1 2 Table 1: General format of the report No Titles Descriptions Titles Times New Roman, 12, BOLD, CAPITAL LETTER Paragraph Spacing (0, 12, 1.5) Body, text, Table Times New Roman, 12, Paragraph Spacing (0, 0, 1.5) Space between Paragraph. ENTER ONE LINES Ensure that the following items are included in the report Introduction Write general information about tensile test (Maximum one page) Objectives of the experiment Write the objectives of the experiment in point form Apparatus used in the experiment List down and write the general information about the required apparatuses to conduct tensile test experiment. Show the diagram/picture of each apparatus. Theory Write down the important theory related to tensile test. Include the necessary mathematical formula applied to analyses the collected data. Test Procedure Write the test procedure used for testing the tensile of the sample. Data collection Summarize in the table the data collected during the lab Results Summarize the results of the tensile test in table form. You might use the table provided to summarize the result. Analysis Show the calculations used to summarize the results. Analyze the stress-strain curve, by diving the force by the original cross- sectional area and elongation by the original length respectively Identify on the plot the elastic from plastic zone of the plot. Identify the yield point for the metal, and list the yield stress in a table. 11
• Identify the maximum tensile strength from the plot, and list the UTS Stress value in at table o Calculate Young’s modulus, yield strength, ultimate tensile strength, fracture strain, % elongation and % area of reduction of the specimen and record on the provided table Discussion o Describe the engineering stress-strain curve for Mild Steel Specimen. • Discuss the experimental results and give conclusions. Find the mechanical properties of the tested material from Handbooks and make comparisons • Discuss the following items. What is the area under the stress-strain curve equivalent to? What does the area under the elastic portion of the stress-strain curve represent? Conclusion References 12
Testometric winTest materials testing machines Analysis SAMPLE TEST TENSILE-1 MATERIAL: mild steel Test Name : TENSILE HCT1-group4 Ref 2 Test Type: Tensile Ref 3 : Test Date : 29/09/2020 13.07 Test Speed : 100.000 mm/min Pretension: Off Sample Length: 61.780 mm Force Elong. Force Elong Energy Stress IN IN Test No Strain Yield Thickness Peak 18.678 6.100 65.370 49.270 7000 5000 GUNOS 3000 2000 1000 001 000 5