Engineering Materials – NOTES – Chapter 8 – Failure

What do we mean by “failure”?

Why does a material fail?

What are the different modes of failure?

How do we select or design a material to minimize the risk of failure?

We will look at two common (and undesirable!) modes of failure: fracture and fatigue.

FRACTURE

Fundamentals of Fracture

Fracture occurs when a material breaks into two or more pieces. This may result from compressive, shear, torsional or tensile loads. Fracture may also be ductile or brittle.

Fracture occurs in two steps: crack formation and then crack propagation.

Why a crack?

A crack creates a stress concentration. The material begins to fail at the stress concentration. For a ductile material, the material fails through cold working and strengthening which makes the crack stable in that it grows slowly. Cracks in brittle material are unstable because the material at the tip of the crack does not cold work and thus cracks will continue spontaneously through brittle material.

Is ductile or brittle failure more desirable and why?

Ductile failure because 1) brittle failure is sudden and catastrophic with no warning and 2) ductile materials are tougher and require more strain energy to bring them to failure.

Ductile Fracture

Ductile materials under tension undergo a series of steps that lead to fracture. These are:

1. Plastic deformation produces necking
2. Small cavities begin to form in the interior of the material
3. The cavities join to form a crack
4. The crack propagates
5. Fracture occurs, typically at a 45 degree angle to the tension as this is the angle of maximum shear stress. (Fig 8.3 shows ductile and brittle fractures)

Brittle Fracture

Brittle fracture shows little if any plastic deformation and is a result of rapid crack propagation. Brittle fracture occurs perpendicular to the applied tension and often has a relatively flat fracture surface. The origin of the crack may be indicated by “V” shaped markings that point toward the origin of the crack, or by a set of lines that radiate outward from the origin of the crack.

Principles of Fracture Mechanics

A basic understanding of how materials fracture (fracture mechanics) will help us understand and better avoid the causes of fractures. It all begins with a stress concentration…

Stress Concentrations

Perfect materials would have much higher fracture strengths (particularly for brittle materials) than are actually observed. Why is the real strength less than theoretically predicted?

Microscopic imperfections in the material (scratches, internal cracks, …) produce a stress concentration at the imperfection. If the stress concentration results in an applied stress that exceeds to maximum allowable for the material, then we have trouble! A ductile material will deform and provide some stress relief at the crack so these materials are more tolerant of imperfections. A brittle material cannot stretch much and the result is rapid failure at stresses below the theoretical values (actually, the material fails around the crack at the theoretical values, but the stress concentration makes the whole material appear to fail at a value less than what it should. These apparent failure values are the ones given as the strength of the material – got that?!)

Fracture Toughness

Fracture toughness is a measure of a material’s resistance to brittle fracture when a crack is present.

The plane strain fracture toughness value, K_Ic, for a material can be used to get an idea of a material’s ability to resist brittle failure. Higher values are more fracture resistant. Some values are given in Table 8.1 and more in Table B.5 in Appendix B. (Examine Table 8.1)

Design Using Fracture Mechanics

In many applications it is useful (even important!) to know how crack size and geometry relates to stress in a material. A variety of nondestructive testing (NDT) methods exist (such as acoustic emissions) that enable us to determine the size of cracks within a material. With this capability, we can specify a maximum allowable flaw size that corresponds to a given stress:

a_c = (1/p)(K_Ic/sY)²

where:

a_c = allowable crack size

s = applied stress

Y = a dimensionless parameter that depends on crack and specimen sizes, geometries, and manner of load application. (sounds like a Ph.D. thesis waiting to happen!) For planar specimens with cracks much shorter than the width, Y has a value of approximately 1.

Design Example 8.1 gives a good evaluation of critical crack lengths for spherical pressure vessels. Note that medium carbon steel has the greatest crack tolerance and is a common material for the construction of pressure vessels (where environmental factors are not a concern).

Impact Fracture Testing (lab)

Material failure may depend on the loading conditions as well as the type of material. One special and significant loading condition is impact loading. Impact loading is used to measure impact energy that can be absorbed by different materials in a standardized test. The two standardized tests are the Charpy and Izod tests. We will be performing a Charpy impact test. Both tests are similar in their execution.

The Test Method

Both tests are performed using a setup as shown in Fig. 8.11. The test steps are as follow:

1. A notched specimen is placed in the machine
2. The “hammer” is moved to a cocked position with a height of h
3. The hammer is released and swings through the specimen, breaking the specimen
4. The height, h’, achieved the hammer after the impact is measured.
5. The impact energy is computed as the difference between the hammer’s initial height, h, and its after impact height, h’.

What impact tests show

A high impact energy indicates a ductile fracture while a low energy indicates a brittle fracture. One important characteristic of materials is the point at which they transition from ductile to brittle fracture under impact loading. This can be determined by running impact tests on the same material at different temperatures. The transition should show up as a relatively sudden drop in impact energy as the temperature of the test specimen decreases (Fig. 8.12). The transition temperature is considered to be the point where the material starts to show a decrease in impact energy and the impact surface begins to exhibit some amount of a shiny granular texture that indicates the presence of brittle failure (see Fig. 8.13).

Why is this important?

The environment were materials is used can affect their behavior. For example, when the Alaska pipeline was constructed in the 1970’s, a Texas oil company took their equipment to the North Slope of Alaska. A number of their machines experienced brittle failure, likely due to the change in failure mode from ductile to brittle.

FATIGUE

What is a fatigue failure? Failures that occur due to repeated loading cycles (alternating loads).

How is it different from static failure?

• Fatigue failure occurs at stresses well below the yield strength of a material.
• Fatigue failure is always brittle and catastrophic in nature with no visible warning prior to failure
• Fatigue accounts for about 90% of all failures in metals.

The early years of understanding fatigue – a story about British railways in the 1800’s.

Cyclic Stresses

Many mechanical engineering designs deal with machines with varying loading conditions. Two important stresses are needed to design for fatigue, the mean stress and the stress amplitude:

mean = s_m = (s_max + s_min)/2 range = s_r = s_max – s_min amplitude = s_a = (s_max – s_min)/2

Failure criteria depend on a combination of the mean stress and the stress amplitude. You will learn much more about the in ME 333 – Design of Machine Elements!

The S-N Curve

S-N curves are generated to represent the failure characteristics of materials under completely reversed loading conditions (s_min = - s_max, s_m = 0). These curves are plotted with the stress amplitude (S) on the vertical scale vs. the log of the number of cycles (N) on the horizontal scale (Fig. 8.17). These curves may be of two different types:

• Materials that have a fatigue limit (such as steel) – The material with a fatigue limit has some stress amplitude below which the material displays infinite life. For a perfect steel sample (polished finish, no stresses concentrations, no environmental or size factors, …) the limit is approximately 0.5 S_UT and occurs at 10⁶ cycles.
• Materials with no fatigue limit (such as aluminum) – The material is continually weakened by the application of a cyclic load. The fatigue limit for these materials is often taken to be their strength at a high number of cycles (10⁸ being a common value).

(Just to understand how many cycles are possible, how many revolutions will a 16” car tire undergo in 100,000 miles? If the engine of the car goes through 2500 revolutions per mile, how many engine cycles are we talking about?)

Crack Initiation and Propagation in Fatigue

Where does fatigue failure begin?

• Failure usually begins on the surface of an object at some discontinuity or imperfection in the surface. This is the crack initiation.
• The crack grows to a critical size without any evidence of plastic deformation in the part.
• Once the crack reaches a critical size, the part fails by sudden fracture.

Factors That Affect Fatigue Life

What factors might change the fatigue life of a material?

Why do these factors affect the fatigue life?

• Existence of a nonzero mean stress: Remember, the S-N curves are developed for a mean stress of zero. A nonzero mean stress will reduce the fatigue life. More on this in ME 333
• Surface effects: Because cracks start at the surface, the quality of the surface plays an important role in setting the fatigue life. Some effects include:
• Design Factors – Geometric discontinuities (keyways, grooves, steps, threads, etc.) provide areas for higher stress concentrations that are more susceptible to fatigue.
• Surface Treatments – The quality of a surface finish determines the number and size of imperfections on the surface. Thus, a polished surface is stronger in fatigue than a ground surface, which is stronger than a machined surface. Shot peening the surface to introduce residual compressive stresses will improve the fatigue strength. Case hardening will have a similar effect.
• Size effects: The size of an object affects its fatigue. Larger objects have lower fatigue strengths
• Environmental effects: Temperature and corrosion may play are role in fatigue failure. Constrained parts that are subject to fluctuating temperatures and repeated thermal expansion-contraction cycles may fail from thermal fatigue even without external mechanical loads.

You might find the two case studies at the end of the chapter (pp221-233) interesting reading!