1. Mechanical Properties: 2
MSC101: Eyres

2. Chapter Learning Objectives
Using energy arguments, explain why flaws in a material may lead to premature fracture
Define fracture toughness and calculate it and the critical flaw size for a material
Define the fracture mechanics relationship between the material properties, the stress applied, and the flaw size
Identify the morphology of failure surfaces that indicate whether ductile or brittle fracture occurred
Describe the process of fatigue
Explain why fatigue occurs and quantify fatigue behavior
Describe the process of creep
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7-1 Fracture Mechanics
Fracture mechanics is the discipline concerned with the behavior of materials containing cracks or other small flaws
The term “flaws” refers to such features as pores, inclusions, or microcracks. It does not refer to atomic level defects such as vacancies or dislocations
Fracture toughness measures the ability of a material containing a flaw to withstand applied load
Fracture toughness may be tested by applying a tensile test to a specimen prepared with a flaw of known size and geometry
The stress applied to the material is intensified at the flaw. The stress intensity factor is given by Equation 7-1, which contains geometric factor f, applied stress σ, and crack size a
By testing, we determine the value of K that causes the flaw to grow and cause failure. This value is defined as the fracture toughness Kc
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4. Fracture Toughness and Resisting Factors
Fracture toughness depends on the thickness of the sample: as thickness increases, Kc decreases to a constant value
This value is called the plane strain fracture toughness Kic
The ability of a material to resist the growth of a crack depends on a large number of factors, some of which are:
Ductility (Kc) or Brittleness (Kc)
Thicker (Kc) or thinner (Kc)
Faster (Kc) or slower (Kc) rate of application of the load
Increasing (Kc) or decreasing (Kc) temperature
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5. The Importance of Fracture Mechanics
Fracture mechanics allows us to design and select materials while taking into account the inevitable presence of flaws
There are three variables to consider:
the size of the flaw, a
the property of the material, Kc or Kic
the maximum stress the material must withstand, σ
If we know (1) and (3), we can select a material with the appropriate fracture toughness to prevent the flaw from growing
If we know (1) and (2), we can calculate the maximum stress a component can withstand and design it to ensure it does not exceed that stress
Finally, if we know (2) and (3), we can calculate the maximum size of a flaw that can be tolerated
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Brittle Fracture
Any crack limits the ability of a ceramic to withstand a tensile stress, because cracks concentrate and magnify the applied stress
The actual stress at the crack tip can be found through Equation 7-3
If the actual stress exceeds the yield strength, the crack propagates
Alternatively, by energy methods, we derive Equation 7-4 for the stress needed to propagate the crack
This is just Eq 7-1 again.
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9. Microstructural Features of Fracture in Metallic Materials
Two aspects of ductile fracture give it distinctive features:
that it occurs in a trangranular (through the grains) manner, with microvoids forming at grain boundaries
that slip also contributes, with the highest resolved shear stress at a 45° angle to the applied stress
Thus a ductile fracture will typically display:
necking with a flat face where microvoids nucleated and coalesced
a small shear lip where the fracture surface is 45° to the applied stress
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Brittle Fracture
A brittle fracture can be identified by features on the failed surface
Normally, the surface is flat and perpendicular to the applied stress
However, if failure occurred by cleavage, each fractured grain is oriented differently, giving the surface a “rock candy” look
Another common fracture feature is the Chevron pattern, produced by separate crack fronts propagating at different levels in the material
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11. Microstructural Features of Fracture in Ceramics and Glasses
In ceramics, the ionic or covalent bonds permit little or no slip, and so failure is a result of brittle fracture
The fracture surface is typically smooth, and frequently no characteristic feature points to the origin of the fracture
Glasses also fracture in a brittle manner. Frequently a conchoidal fracture surface is observed. This surface contains a smooth mirror zone near the origin of the fracture and tear lines comprising the remainder of the surface
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Fatigue
Fatigue is the lowering of strength or failure of a material due to repetitive stress that may be above or below the yield strength
Fatigue failures typically occur in three stages:
A tiny crack nucleates, often well after loading begins
The crack gradually propagates as the load continues to cycle
A sudden fracture occurs when the remaining cross- section is too small to support the load
Fatigue failures are often easy to identify by the characteristic features they leave on the fracture surface (see Figure 7-15)
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Fatigue Test
One method for testing a material’s resistance to fatigue is the rotating cantilever beam test, pictured to the right
In the test, the stress at any one point on the specimen goes through a complete sinusoidal cycle from maximum tensile to maximum compressive stress
The results of such a test are usually presented in a S-N curve (also known as the Wöhler curve), as seen to the right
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14. Results of the Fatigue Test
The fatigue test can tell us how long a part may survive or the maximum allowable loads that can be applied without causing failure
The endurance limit is the stress below which there is a 50% probability that failure by fatigue will never occur. It is the preferred design criterion, though it should be treated with caution since research has shown that it does not exist for many materials
Fatigue life tells us how long a component will last at a particular stress
Fatigue strength is the maximum stress for which fatigue will not occur within a particular number of cycles
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15. Creep, Stress Rupture, and Stress Corrosion
Creep is time-dependent, permanent deformation under constant load or constant stress and at high temperatures
A material is considered failed by creep even if it has not fractured. When a material does creep and then ultimately breaks, the fracture is called a stress rupture
Stress corrosion is a phenomenon in which materials react with corrosive chemicals in the environment. This leads to the formation of cracks and the lowering of strength
Tempering glass produces an overall compressive stress on the surface of the glass and prevents cracks from growing
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