Lab 1 - Tensile Testing of Isotropic Materials

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Jan 9, 2024

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Tensile Testing of Isotropic Materials Lab 1 – Aditya Kannan Introduction The objective of this lab report is to understand the utility and results of tensile testing a material. Using an Instron tensile testing machine and a digital image correlation simultaneously, we obtained data to observe the stress vs strain for a given piece test specimen made of 5052 aluminum alloy. Part 1: Instron Tensile Tester Discussion of relevant concepts Engineering constants relevant to this experiment An isotropic material is characterized by its mechanical properties being independent of direction, meaning it exhibits the same behavior in all directions. The relevant constants for isotropic materials include Young's Modulus (E, Pascals), Yield Point, Shear Modulus (G), and Poisson's Ratio (ν). Young's Modulus measures the material's stiffness in tension, while Shear Modulus quantifies its resistance to shear deformation. Poisson's Ratio describes the material's tendency to contract laterally when stretched longitudinally. Stress-strain curve Figure 1: A common stress/strain curve By Nicoguaro - Own work, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=89891144 The stress-strain curve typically exhibits several distinct regions: • Elastic Region : In this initial phase, the material behaves elastically, meaning it returns to its original shape when the load is removed. Young's Modulus (E) can be determined from the slope of this linear region, reflecting the material's stiffness. • Yield Point : Beyond the elastic region, the material enters the plastic deformation phase. The yield point signifies the stress at which plastic deformation begins.

• Ultimate Tensile Strength: This is the point on the curve where the material reaches its maximum stress before necking or localized thinning occurs. Ultimate Tensile Strength (UTS) is the highest stress the material can endure under tension. • Fracture Point: The curve terminates at the fracture point, indicating the stress at which the specimen ruptures. Experimental setup First, the crossectional area of the sample was found by measuring the width and thickness using a pair of calipers. Then, the 5052 aluminum alloy specimen, prepared in a dogbone shape, was securely clamped into the testing machine. The data recording was started on the testing machine and a constant tensile load was applied along the axis of the specimen at a controlled rate while the machine measured the corresponding deformation via the crosshead displacement. Part 2: Digital Image Correlation (DIC) Discussion of relevant concepts Digital Image Correlation (DIC) is a non-contact optical measurement used to analyze the deformation and strain distribution on the surface of a specimen subjected to mechanical testing. DIC works by tracking the displacement and deformation of small subsets or "speckles" on the specimen's surface. These speckles serve as natural or applied markers that can be tracked between images taken before and during deformation. While DIC is capable of tracking deformation on both axes, we are only using data in the y-axis for this report. Experimental setup A camera was carefully positioned to capture images of the specimen's surface, and proper lighting and focusing were ensured to obtain a clear video. The speckle pattern on the sample was pre-applied via a spray by the lab assistant. To begin the experiment, we began recording via the software the camera was configured with. Post-capture, the footage was used to analyze deformation. The software compared the reference image with the pre-defined deformed images, tracking the displacement and deformation of individual speckles. From the displacement data, strain fields across the specimen's surface were computed, providing us with deformation data on a selected region of the sample. Results The crossectional area of the sample was measured to be 7.28 𝑚𝑚 2 or 7.28 ∗ 10 −6 𝑚 2 . The length of the sample is 31.33 𝑚𝑚 or 3.13 ∗ 10 −2 𝑚 . The data from the tensile testing machine was received in the form of crosshead displacement ( 𝑚𝑚 ) and force ( 𝑘?? ). From the data obtained from the DIC, the y-axis displacement measurements were used. Strain values were calculated by converting 𝑚𝑚 to 𝑚 and dividing by the length of the sample. Stress values were calculated by converting 𝑘?? to 𝑁 and dividing by the crossectional area of the sample. Since DIC does not yield stress measurements, the force data from the tensile testing machine was extrapolated and correlated with the displacement data of the DIC to provide the graphs below. The consolidated experimental data obtained from the testing machine and DIC is plotted in the graph below.

The Youngs Modulus was calculated by finding the slope of the linear (elastic region) between 0 𝑃𝑎 to 2.75 ∗ 10 −8 for the Instron tensile testing machine data and 0 𝑃𝑎 to 2.76 ∗ 10 −8 𝑃𝑎 for the DIC data. Below are graphs of the elastic region from both data sources with treadlines plotted. Instron Tester DIC Youngs Modulus 1.82 ∗ 10 10 𝑃𝑎 6.86 ∗ 10 10 𝑃𝑎 Yield Point 5.946 ∗ 10 −4 𝑚 4.34 ∗ 10 −3 𝑚 Ultimate Tensile Strength 3.38 ∗ 10 8 𝑃𝑎 3.37 ∗ 10 8 𝑃𝑎 Fracture Point 3.36 ∗ 10 8 𝑃𝑎 3.36 ∗ 10 8 𝑃𝑎 Table 1: Results from both data sources 0.00E+00 5.00E+07 1.00E+08 1.50E+08 2.00E+08 2.50E+08 3.00E+08 3.50E+08 4.00E+08 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Stress (Pa) Strain (m/m) Stress-strain curve Instron Tester DIC y = 1.82E+10x + 1.51E+07 R² = 9.90E-01 0.00E+00 5.00E+07 1.00E+08 1.50E+08 2.00E+08 2.50E+08 3.00E+08 3.50E+08 -0.01 0.00 0.01 0.01 0.02 0.02 Stress (Pa) Strain (m/m) Elastic region (Instron Tester) y = 6.86E+10x + 4.83E+07 R² = 9.95E-01 0.00E+00 5.00E+07 1.00E+08 1.50E+08 2.00E+08 2.50E+08 3.00E+08 3.50E+08 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 Stress (Pa) Strain (m/m) Elastic region (DIC)

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Discussion The fracture surface was not normal to the direction of loading due to aluminum's ductility. Ductile materials like aluminum undergo plastic deformation before fracturing, causing localized necking and misalignment of the fracture surface with the loading direction. Below is Hooke’s Law for 1D and 2D plane stress specimens: 1D: 𝜎 = 𝐸𝜀 2D: [ 𝜎 ? 𝜎 ? 𝜏 ?? ] = [ 𝐸 ν 0 ν 𝐸 0 0 0 𝐸 2(1+ν) ] ∙ [ 𝜖 ? 𝜖 ? 𝛾 ?? ] An extensometer directly measures strain on the specimen's surface, providing more precise strain data than crosshead movement measurement of a testing machine. It contributes to accuracy by eliminating machine compliance, offering localized measurements and reducing errors in strain data. Possible sources of errors Machine compliance, misalignment, strain localization, temperature fluctuations, specimen preparation, data acquisition, and anisotropic material behavior. Advantages & Disadvantages of Digital Image Correlation (DIC ) Advantages: Non-contact measurement, high spatial resolution, full-field strain measurement, and applicability to various materials. Disadvantages: Complexity of setup and calibration, surface preparation, computational intensity, limited to surface measurements, and sensitivity to environmental factors.