= Tensile modulus experiment
MIT's Spring 2004 laboratory assignment Properties of Heat Treated Steel gives a concrete <tensile testing> protocol. Record transducer channels and calibration factors; measure specimen diameter and length, and the <extensometer> <gauge length> with its locking pin inserted. Zero the <load cell>, pin the threaded grips into their adapters, and attach the <extensometer> centrally. Apply the specified seating load, record actuator position, then acquire readings every second while moving at about $0.05\ \mathrm{cm\,min^{-1}}$. The handout derives <engineering stress> from <load cell> <force>, <engineering strain> from <extensometer> deformation, and <Young's modulus> by <linear regression> below the <proportional limit>; it warns that actuator-derived <strain> includes apparatus deformation.<Properties of Heat Treated Steel by Massachusetts Institute of Technology>[Laboratory assignment 10, printed pp. 2–3: Procedure for Tension Tests; Calculations]{ref}
For a modulus-focused measurement, select a load window after seating, hold <temperature> and loading rate consistent, and record <force>, local extension and <crosshead displacement> together. Fit $F=F_0+k_g\Delta L_g$ within that window and calculate $E=k_gL_g/A_0$. Inspect the <regression residuals> for curvature; repeat at a lower maximum load and include unloading to check <elastic deformation>. These are diagnostic additions to the cited protocol, whose full test continues through failure. The handout's seating load is specific to its specimens and apparatus, rather than a universal preload.
\Image[/tensile-modulus-apparatus-and-displacement.png]
{title=Three readouts in a tensile experiment: force, local extension and actuator travel}
{description=Original functional schematic. The load cell reads the axial force; two extensometer contacts define the gauge length inside the specimen. A separate actuator displacement readout spans a load path that includes the specimen and deformable grips and frame. The adjacent series model separates specimen extension from machine extension. Shapes are schematic and are not a dimensional reconstruction of MIT's apparatus.}
An <extensometer> measures the change between its contact points; <crosshead displacement> measures travel of the machine's moving member. The manufacturer Instron explicitly distinguishes local <strain> from travel that includes machine deformation and <machine compliance>.<Static Axial Clip-On Extensometers by Instron>[FAQs: How does a clip-on extensometer work?; When should I use a clip-on extensometer instead of crosshead displacement?]{ref} The <gauge length> $L_g$ can be shorter than the uniform length $L$ between grips. Thus even a perfectly rigid machine generally has $\Delta L_g\ne x$: the local instrument sees only its own segment. Do not divide one channel's extension by the other channel's reference length.
Grips must transmit axial <force> without slip. Misalignment adds <bending moment> and makes opposite sides experience different axial <strains>; an instrument on just one side may then report a biased modulus. A changing extension offset, hysteresis between loading and unloading, or load-dependent fitted slope is evidence to investigate seating, slip or material response. A straight line over a short interval alone does not identify which is responsible.
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