TENSILE TESTING PRACTICAL

Transcription

1 TENSILE TESTING PRACTICAL MTK 2B- Science Of Materials Ts epo Mputsoe

2 Summary Material have different properties all varying form mechanical to chemical properties. Taking special interest in mechanical properties alone, we can physically test and quantify such properties. The properties vary from how brittle or ductile a material is to how much energy it can absorb before it breaks. The experiment employs this physical approach in testing for mechanical properties of metals and attempting to quantify these properties so that it provides a platform in which different material strengths can be compared against each other. List of Contents Aim of practical... 2 Introduction... 2 Stress (σ)... 2 Strain (ε)... 2 Elastic modulus (E)... 2 Yield Strength... 3 Tensile strength... 3 Elongation (ductility)... 3 Resilience... 3 Toughness... 3 Results... 4 Raw Data... 4 Processed Data... 4 Interpretation and Discussion of Results... 5 Ductility... 5 Plasticity... 6 Yield Stress... 6 Worst Case graph... 7 Tensile Strength... 7 Modulus of resilience... 7 Modulus of Toughness... 8 Conclusion... 8 Appendix... 9 Bibliography

3 Aim of practical To determine mechanical properties for a material from a stress strain test. Introduction Materials behave differently when exposed to mechanical loads. To quantify these properties and enable comparison between materials, standard quotients and integrals have been derived. The functions are explained as follows: Stress (σ) This is just a quantification of the load per unit area of the material with quotient: σ = F [1] A Where: F= Load applied A= Area on which the load is subjected Strain (ε) A material under loading will experience a deformation. Strain is a measure of the amount of deformation an object experiences. [1] ε = l extended L original L original Where: L original is the original length of the specimen l extended is the extended length of the specimen Elastic modulus (E) This is a measure of the proportionality between the stress and the stress on a specimen. The ratio is calculated: E= σ ε 2

4 Yield Strength A specimen under loading will experience a constant ratio of strain due to stress until a limit is reached where the material becomes permanently deformed and does not display elastic properties. [1] This is the yielding point of the material and the strain that causes it is called the yield stress and thus the yield strength of the material. Tensile strength After the specimen has reached yield strength, it will continue to experience strain without any increase in the stress. This will continue until it has yielded and will experience strain hardening which is an increase in both the stress and the strain but does not follow the proportionate relationship of the first stage. It will continue to display these properties until it reaches the ultimate tensile strength after which the material will begin necking. [1] Elongation (ductility) Necking continues until the material ultimately fractures. The elongation is thus, the stress at the fracture point. Resilience In the proportional limits of the stress to strain, work is done by the load on the specimen. This implies therefore, that energy is tranferred to the specimen and is related to the strains of the specimen. This energy is comprehended in terms of the energy density of the specimen which is the amount of strain energy per unit volume of the material. The totality of the strain energy density in the limits of proportionality is then referred to as the resilience of the specimen. [1] Toughness The toughness is the total amount of strain energy the material can absorb just before it fractures. This is therefore the total amount of energy within and beyond the proportional limit until the fracture point. 3

5 Results Raw Data Force (kn) Guage Length(mm) Processed Data Guage Extension Stress Strain Length(m) (m) E E

6 Stress (Pa) T.S.L Mputsoe Graph of Stress versus Strain 1.2E+09 1E Stress versus strain graph OFFSET Strain at fracture Ultimate Tensile Strength Poly. (Stress versus strain graph) Linear (OFFSET) Linear (Strain at fracture) Linear (Ultimate Tensile Strength) Strain (m/m) Interpretation and Discussion of Results Ductility The data produces a standard stress strain curve particular with ductile materials. To quantify the ductility of the material, it will be expressed as a percentage so that it is easily comprehensible. This is achieved by expressing the strain at fracture point as a percentage. Percentage elongation= (ε f 100) = % = 21.5% 5

7 This implies that the material elongated by 21.5% of its original length which is a considerable extension in length and hence a fitting justification to the affirmation that it is a ductile material. Plasticity It is also a largely plastically deformable material up to stresses of about 600MN where the material starts to yield. The modulus of elasticity is approximated to be 21GPa. These figures are obtained from the stress strain graph where the modulus of elasticity is obtained through the 0.2% offset method. Notice however that four of the six initial data points that build up the graph fall off the best fit line. Estimation of the elastic region therefore exploits only two of the six possible data points. That is only 33% of the possible data. It is therefore highly inaccurate with an uncertainty value of 77%. The modulus of elasticity could therefore be anything between 37.17GPa to 16.17GPa. That is a huge deviation of 21GPa which is 100% of approximated value itself. The spreadsheet however feeds back an R 2 value of which is reasonably close to 1. Take then, nothing away from the precision of the best fit line. The large discrepancy is only in the initial values of the graph with a 100% alignment with the remaining data points. Yield Stress The approximated yield stress is definitely affected by the inaccuracy in the starting values. The inaccuracy however is not as large as that in the plasticity of the material. To quantify the inaccuracy of the yield stress, we analyze the worst case graph which is represented in diagram. The worst case graph does not consider the standard graphs that display mechanical properties and only the precision in the number of data points covered by the graph. That is to say, the worst case graph optimizes the number of data points covered by best fit curve. The Worst case graph feeds back a yield stress value of about 664MPa while the best fit approximation was 600MPa. This is a deviation of only 10.7%. The deviation in itself is practically a lot less than 10.7% due to the impossibility of the shape of the graph. The worst case graph in in violation of the standard, observed behavior of metals. It suggests that the material experiences increasing strain under a reducing amount of stress after it has yielded and yet consequently to that, reaches another stage where it undergoes strain hardening. There is no material that displays such properties and thus is simply due to the inaccuracy of the set of data in the beginning stages of the graph. 6

8 Strain T.S.L Mputsoe Worst Case graph Worst Case graph R² = E+09 1E Stress Tensile Strength The best fit graph reflects an ultimate tensile strength of 1.04 GPa while the worst case graph feeds back a value of l.06 GPa. There is thus a discrepancy of just 1.2% in the two values. This goes to emphasize the accuracy of the final half of the graph as observed from the exceptional alignment of the best fit curve with the last portion of the data values on the graph. Modulus of resilience The modulus of resilience is calculated as the area of the graph in the proportional region. To calculate this, the trapezoidal formula was used in a spreadsheet to calculate the area. The area was therefore determined to be 8.83MJ/m 3. The material can therefore absorb an approximation of 8.83MJ/m 3 before it deforms permanently. The figure is not precisely 8.83MJ/m 3. It could be understated considering that the system would not be closed to interaction with the environment if it so happens that the material is exposed to loading of the stated amount of density. Energy could be lost as thermal heat to the environment during the interaction and hence more energy may be loaded onto the material before it permanently deforms. 7

9 Modulus of Toughness As opposed to the modulus of resilience, the modulus of toughness encompasses the totality of the area of the stress strain graph. A similar approach to that which was employed in calculating the modulus of resilience was used to calculate the modulus of toughness. That is to say, the trapezoidal method was used to calculate the total area. It was approximated to be 48.6 MJ/m 3. This implies that the material may absorb energy densities of up to 48.6 MJ/m 3 before it fractures. Conclusion The material that was tested to have properties: Elastic Modulus: 21GPa Yield Strength: 600MPa Tensile Strength: 1.04 GPa Elongation: 21.5% Resilience: 8.83MJ/m 3 Toughness: 48.6 MJ/m 3 The material is then identified to be a stainless steel alloy. This is because of the extensively elastic properties and yet incredible tensile strength. The stainless steel has been enriched with properties that allow it to be shapeable and yet strong enough to resist stress. Stainless steel alloy properties vary greater and therefore it is hard to find a metal alloy with properties that are exactly in line with the properties observed from the specimen. It would have aided in identifying the metal if the metal was tested for composition and the dominant compositor identified. It is a close to impossible task attempting to identify a non- pure specimen from mechanical properties alone as mechanical properties are not necessarily generic to a single type of material. The properties vary greatly due to factors such as wear and slight impurities embedded in the material. The experiment is therefore inconclusive in terms of identifying the metal but nonetheless is a very accurate experiment in terms of investigating mechanical properties alone. Despite the large variation in the initial set of data points that build up the graph, it revealed to be highly accurate on the determination of the: Yield stress Tensile Stress Toughness Resilience The inaccuracy was reflected extensively in the determination of the modulus of elasticity alone and is only one of the six properties that were subject to investigation. All in all therefore, the experiment is highly accurate and precise. 8

10 Appendix Forc e (kn) Guage Length(m m) Guage Length( m) Extensi on (m) Stress Strain Derivat ive Area(mm^2) Integra l E Area(m^2) E Yield Strength MN Tensile Strength Pa Stress At Fracture Point Summ ation s Bibliography [1] R. Hibbler, Mechanics Of Materials, Boston: Pearson,

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