Strength fracture

Any reverse engineered part shall never operate beyond its fracture strength. The complexity of fracture mechanism prevents engineers from developing 

Cohesive tensile strength is based on the theory that estimates fracture strength in tension. The atoms of crystalline metals are bound together by 

Consider an infinitely wide plate subject to an average tensile stress a, with a thin elliptical crack of length 2c and a radius of curvature at its tip of p  

Assume that the theoretical cohesive strength can be reached at the crack tip, while the average tensile stress represents the nominal fracture strength, Gjr. Set Equations 3.15 and 3.16 equal to each other then the nominal fracture strength can be calculated by Equation 3.17  

The sharpest possible crack has a radius of curvafure af fhe fip equal fo fhe atomic disfance, p( = a , and fhe fracfure sfrengfh can be approximated by Equafion 3.18  

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Ahoy Fracture strength. O, GPa Density, p, mg/m Specific strength, o/p Young s modulus, E, GPa... 

Strength. The fracture strength of vitreous sihca depends on its surface quaUty, which can be affected by thermal treatment and handling conditions. Microcracks, surface contamination, and crystallisa tion can reduce the strength from the value of pristine vitreous sihca by several orders of magnitude. 

Fig. 5c. Relation of T-curve to crack growth and strength (c) fracture strength as a function of crack size showing region of flaw size tolerance.

Orowan (1949) suggested a method for estimating the theoretical tensile fracture strength based on a simple model for the intermolecular potential of a solid. These calculations indicate that the theoretical tensile strength of solids is an appreciable fraction of the elastic modulus of the material. Following these ideas, a theoretical spall strength of Bq/ti, where Bq is the bulk modulus of the material, is derived through an application of the Orowan approach based on a sinusoidal representation of the cohesive force (Lawn and Wilshaw, 1975). 

Fig. 17.2. Tests which measure the fracture strengths of ceramics, (a) The tensile test measures the tensile strength, CTj. (b) The bend test measures the modulus of rupture, o , typically 1.7 x CTj. (<) The compression test measures the crushing strength, a, typically 15 x...

There are two, and they are complementary. The tensile fracture strength (Chapter 17) is roughly... 

In any structural application it is the peak stress which matters. At the peak, the fibres are just on the point of breaking and the matrix has yielded, so the stress is given by the yield strength of the matrix, d and the fracture strength of the fibres, (t, combined using a rule of mixtures... 

Tills is shown as the line rising to the right in Fig. 25.3. Once the fibres have fractured, the strength rises to a second maximum determined by the fracture strength of the matrix... 

Fig. 25.4. Load transfer from the matrix to the fibre causes the tensile stress in the fibre to rise to peak in the middle. If the peak exceeds the fracture strength of the fibre, it breaks.

A composite material for a car-repair kit consists of a random mixture of short glass fibres in a polyester matrix. Estimate the maximum toughness of the composite. You may assume that the volume fraction of glass is 30% the fibre diameter is 15 pm the fracture strength of the fibres is 1400 MPa and the shear strength of the matrix is 30 MPa. 

Natural ice has large grains typically 10 mm or more (it is like a casting which has solidified very slowly). Then this equation gives a tensile fracture strength of 1 MPa -precisely the observed strength. So when ice is loaded in tension, it creeps when the stresses are less than 1 MPa the strength is limited to a maximum of 1 MPa by fast fracture. 

Its = tensile strength parallel to fibres d] = fracture strength of fibres d = yield strength of matrix. 

Fig. 16. Fracture strength versus crack length diagram illustrating the failure / non-failure boundary for fracture of a nuclear graphite.

In which we summarize the terms as CTq = cohesive fracture strength of A = modulus of A, h = thickness of A layer L = influx length to a maximum length Lc, I — influx coverage of the A-B interface (/ < 1) = fraction of elastic energy dissipated in the A layer ( < 1). 

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