exl graph (engineering) in a lab report

Alrashaid 1

Alrashaid 2

Alrashaid 3

Theories:

Engineering Stress : σ = P/A0,

True Stress : σ T = P/AT, σ T = σ (1+ ϵ ).

True Stress: ϵ = (lf – l0) / l0.

True train: ϵ t = ln (li/l0) = ln (1+ ϵ).

Precent elongation= ((lf – l0) / l0) *

Precent Error = ((|Experimental Value – Theoretical Value|)/Theoretical Value)*

Modulus of elasticity E = slope of young’s modulus line in stress vs strain curve

Discussion:

By observing the stress-strain curves the different tensil properties for the various tested materials can be seen. The material with the largest ultimate tensile strength is steel shown in Figure 1. What can be noticed on the curve of this particular specimen is the the wavey distortions before the curve reaches the ultimate tensile stress. This is due to the properties of steel in which some discontinuities within the grain structure and impurities within the sample are formed which yielded almost constant strain under the increasing tensile load. This happens with the aluminun sample but in a lesser manner. Steel also experiences more necking before failure comparinng it with the Aluminum sample. It can be cunclueded that Aluminum was more brittle than steel. Both polymers LDPE and HDPE have a largees plastic region, which means they deforem a lot more before faluir accures in comparison with thhe steel and aluminum sample. This can be seen in figures 3 and 4 The table below shows all the calculations done that helped in forming the graphs.

Specimen	Width (in)	Thickness (in)	Area (in^2)	Lo	Lf	%Elongation
Steel 1018	0.503	0.125	0.062875	3.79	4.7050955	24.145
LDPE	0.839	0.129	0.108231	3.75	10.2133125	172.355
Al 2024	0.505	0.127	0.064135	3.75	4.5742125	21.979
HDPE	0.737	0.12	0.08844	3.75	10.3402875	175.741

Fail load (lb)	ENG stress (psi)	Strain (psi)	ENG strain (psi)	True strain	True stress
3985.367	63385.55865	17.14908	0.1714908	0.158277126	74255.59881
152.1301	1405.605603	19.40467	0.1940467	0.177348126	1678.358732
4111.328	64104.28003	20.44067	0.2044067	0.185987081	77207.62437
343.628	3885.436454	12.256	0.12256	0.115611791	4361.635546

Young’s modulus for the matrials was alos calculated. This was done by taking the slope of young’s modulus line in stress vs strain curve shown in figures 1, 2, 3, and 4. The calculated values were campared to the given values and the error was obtained. The below table shows the results :

Material	Calculated Modulus	Given Modulus	Error %
1018 steel	1940785.802	29000000	93.30764
2024 Aluminum	212019.4049	1000000	78.79806
LDPE	30897.88491	80000	61.37764
HDPE	159807.4659	145000	10.21205

Figures:

Figure 1: Stress-strain curve for 1018 Steel

Figure 2: Stress-strain curve for 2024 Aluminum

Figure 3: Stress-strain curve for LDPE

Figure 4: Stress-strain curve for HDPE