Concept explainers
The stress at which first crack is formed in the composite under isostrain condition.
Answer to Problem 84AAP
The stress at which first crack is formed in the composite under isostrain condition is on
Explanation of Solution
Write the expression to calculate strain on the composite
Here, stress on the composite is
Write the fracture-toughness equation for the composite.
Here, fracture-toughness of the composite is
For the isostrain conditions, the strain on the composite will be equal to strain on the matrix and strain on the fiber respectively.
Here, strain on the
Considering the
Here, fracture-toughness of the
Considering the
Here, fracture-toughness of the
Conclusion:
Substitute
Substitute
When compared to
Thus, the stress at which first crack is formed in the composite under isostrain condition is on
Want to see more full solutions like this?
Chapter 12 Solutions
Foundations of Materials Science and Engineering
- A discontinuous fibre reinforced composite consists of 20mm long carbon fibres in a polymer matrix. The volume fraction of the composite is 0.5, interfacial shear strength 5MPa and the critical fibre length 2.5mm. The fibre modulus is 250GPa and strain to failure 1.5%. The matrix modulus is 3.5GPa and failure strain 10%. Calculate the tensile strength of the composite in the fibre direction. Answer: 3564arrow_forwardWhen a viscoelastic material is loaded and unloaded, the unloading curve is different to the loading curve, i.e. it takes more energy to displace the material than it does to return the material to its original configuration. This is known as: Select one: O a. creep O b. stress relaxation O c. hysteresis d. strain-rate dependancearrow_forwardWhen choosing a polymer for fatigue crack propagation resistance, would you typically select an amorphous thermoplastic, a semicrystalline polymer, or a heavily crosslinked material? Other than crystallinity and cross-linking, what characteristic of a polymer can have a profound effect on FCP rate?arrow_forward
- Silica (silicon oxide) space shuttle tile is bonded to silicone adhesive. (Look up the CTE for both materials). Assume that the strain at the interface between the silica and the silicone can be calculated from the difference in the CTE’s. Calculate the strain at the interface and the stress at the interface when the adhesive/silica interface is heated from 298 K to 348 K. The silicone adhesive is brittle. Will the adhesive crack, given the aforementioned data?arrow_forwardA continuous-aligned composite lamina is to be designed to have Ec,L= 200 GPa, Ec,T = 10 Q3. GPa and o*c,L = 500 MPa. The desired failure strength of the fiber and matrix are o*f = 1000 MPa and o'm = 20 MPa. Calculate the following to design a composite lamina of desired stiffness and strength; (a) fiber and matrix volume fractions (b) fiber and matrix elastic modulus (c) load fractions of fiber-composite and matrix-composite (d) the calculated stiffness of fiber and matrix correspond closely to which type of fiber and matrix materialsarrow_forwardProblem 4 Calculate the tensile modulus of elasticity of a unidirectional carbon-fiber-reinforced-plastic composite material that contains 64 percent by volume of carbon fibers and is stressed under isostrain conditions. The carbon fibers have a tensile modulus of elasticity of 54.0 × 10° psi and the epoxy matrix a tensile modulus of elasticity of 0.530 x 10° psi.arrow_forward
- Give an approximate value for the tensile strength of a Boron/Aluminum composite with Vf = 0.4. Aluminum 2024 has E = 71 GPa, Poisson = 0.334, yield strength Sy = 76 MPa, strain-to-failure Ey = 22%. Boron fibers have E = 400 GPa, strength = 3.4 GPa, Poisson = 0.25. a. Compute F1t, assuming the Aluminum matrix remains elastic up to failure. If the value found is larger than Sy, the matrix yields, thus invalidating the assumption. b. Recompute using O1 = VfOf + (1 - Vf)Om c. Check that the strain-to-failure is not exceeded.arrow_forwardGlass fibres provide longitudinal reinforcement for a nylon material subject to tensile load. The fibre diameter is 20 μm and the volume fraction is 0.45. (Take Young’s modulus of glass fibres as 70 000 MPa and nylon as 2800 MPa)(i)Calculate the Young’s modulus of composite(ii)Determine the tensile strength in the glass fibre if the tensile strength of the composites and matrix is 14 MPa and 11.8 MPa, respectivelyarrow_forwardA freshly manufactured glass fiber (100μm diameter) is found to break under a 40N tensile load. A similar fiber is subjected to typical handling (causing "wear and tear"). This second fiber is found to break under a tensile load of 0.15 N Assume that the first fiber was defect free, but that the second fiber broke at the lower load due to the presence of an atomically-sharp surface crack that resulted from the handling. Calculate the length of that crack. Your answer should be in units of microns, μmarrow_forward
- A panel of poly(methyl methacrylate) is bolted in the long direction only at 50°C between two other components with zero coefficients of expansion. What is the stress on the polymer at 0°C? Will the polymer break?arrow_forwardQuestion 2: [Strain Energy] A composite rod is comprised of an EN8 steel shaft of length, diameter and Young's modulus of 200 mm, 20 mm and 210 GPa, respectively, that is joined end to end to an aluminium shaft of length, diameter and Elastic modulus of 150 mm, 30 mm and 80 GPa, respectively. If the composite rod stores a strain energy of 20 Nm and deforms linear elastically, calculate: The stresses in each rod. The strain energy absorbed by each component shaft. The elongation of the composite rod. The impact load (F) required to induce this strain given the strain energy stored by the composite shaft, if it falls freely through a height (h) of 150 mm.arrow_forwardQuestion 4 Figure 3 shows the impact of temperature and stress on mechanical properties of materials (a) 1200 High temperature or high stress (b) 900 Medium temperature or medium stress Brittle Ductile Low temperature or low stress 600 300 +Transition temperature -80 -40 40 80 Time Temperature (°C) Figure 3 (a) Izod impact test results for nylon thermoplastic polymer. (b) Creep test results Using Figure 3, explain: (a) The dependence of failure modes on temperature. (b) The effect of temperature changes and stress on the creep rate. Impact strength (J/m) Strainarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY