The composition of the Al-Li alloy needs to be determined. Whether it is hypereutectic and hypoeutectic needs to be explained. Concept introduction: A substance's homogeneous mixture that melts or strengthen at a temperature below either constituent's melting point is a eutectic system. The eutectic temperature for the part species concerned is the lowest melting temperature that is possible over the all combining proportions. It is likely to categorize eutectic systems as hypoeutectic or hypereutectic. The compositions having smaller percentage of β species and greater composition of a than eutectic composition are kniown as hypoeutectic compositions. On the other hand, hypereutectic solutions have a higher β composition and lower a composition than eutectic composition.

Question

For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to a(t) = a(0) exp(-4) (15.10) where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) after 30 s.

Answer 1

Question

Chapter 11, Problem 11.36P

Interpretation Introduction

Interpretation:

The composition of the Al-Li alloy needs to be determined. Whether it is hypereutectic and hypoeutectic needs to be explained.

Concept introduction:

A substance's homogeneous mixture that melts or strengthen at a temperature below either constituent's melting point is a eutectic system. The eutectic temperature for the part species concerned is the lowest melting temperature that is possible over the all combining proportions. It is likely to categorize eutectic systems as hypoeutectic or hypereutectic.

The compositions having smaller percentage of β species and greater composition of a than eutectic composition are kniown as hypoeutectic compositions. On the other hand, hypereutectic solutions have a higher β composition and lower a composition than eutectic composition.

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For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to a(t) = a(0) exp(-4) (15.10) where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) after 30 s.

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For the flows in Examples 11.1 and 11.2, calculate the magnitudes of the Δ V2 / 2 terms omitted in B.E., and compare these with the magnitude of the ℱ terms.