It may be necessary to conduct physical tests to determine
if the mechanical properties of the materials involved conform to
specifications. Hardness, tensile strength, impact, fatigue resistance, wear,
flexibility and many other physical tests are relatively common. These tests
often compare the material in the failed component with standards. Test
specimens for determination of mechanical properties should not be taken from
areas of the component that have been plastically deformed during the failure. In general, structural members and machine parts can fail
to perform their intended functions by:
(reference: Dr. Zee)
excessive elastic deformation (deflection under applied loads),
yielding (permanent material deformation as a result of stress), or
For instance, the deflection of closely mating machine parts due to surface stresses (elastic deformation) can degrade adjacent parts by increasing wear and in certain cases can promote complete failure. A study of the mechanical properties of the parts can provide information on load-bearing capabilities of the system and can minimize such failures.
2. Finite Element Analysis
The finite element method is a powerful numerical tool for analyzing mechanical components and systems. The representation of a component or system mathematically with finite elements generally involves a discretization of the structure into many small pieces, e.g. small brick-like elements (hence the name of the method). The solution to the equations that govern the behavior of the structure is approximated on each and every brick. The collective effect of all the bricks is taken into account during a step that synthesizes the solutions for each brick into one solution valid for the entire structure. This global solution represents the solution to the equations that govern the structure's behavior.
The finite element method provides a tool to predict and evaluate component response, elastic or non-linear plastic, subjected to thermal and structural loads. Thermal analyses may include convection, conduction, and radiation heat transfer, as well as various thermal transients and thermal shocks. Structural analyses may include all types of constant or cyclic loads, mechanical or thermal, along with non-linearities, such as opening/closing of contact surfaces, friction, and non-linear material behavior. Finite element analysis can be used during a failure study in such ways as:
• Predicting the response of an existing component or assembly to stress
• Assessment of remaining life of a component or assembly
• Determining the failure mode of a failed component or assembly, e.g. fatigue, creep, and buckling.
• Designing of a new component or assembly as a part of recommendations for remediation of the problem
3. Fracture Mechanics
Using the many analytical techniques above will help to determine how the part in question actually failed, what the mode of failure was and where the failure was initiated. What is missing is a quantitative idea of the stress environment in the failure and the response of the failed part to that stress. The relatively new science of fracture mechanics can provide a quantitative framework within which the failure may be understood.
Fracture mechanics relates the size of flaws in a material, principally cracks, to the applied stresses on those cracks and to the “fracture toughness” of the material, or its resistance to cracking.
Fractures include both initiation and growth phases. After initiation, perhaps at a pit or some other site of stress-concentration, the crack will only grow when the stresses at the crack tip exceed a critical value known as the “fracture toughness” or KIc. If KIc and the stress conditions are known for a given material, then it is possible to calculate the size of crack that can be tolerated in that material without having the crack grow further. The following equation shows those conditions. A crack will propagate if:
where σ (sigma) is the fracture stress, β (beta) is a dimensionless shape factor and a is the crack length for a crack with only one tip (i.e., not an internal crack, but one opening at a surface). Handbooks for engineering calculations have tables of values for Beta for different geometries.
If the fracture toughness of the material is known, the fracture stress or critical crack size of a component can be calculated if the stress intensity factor is known.
This calculation will allow
• the determination of “permissible flaw size,”
• the calculation of the stress necessary to cause catastrophic failure
• the determination of the load on a component at the time of failure
• the determination as to whether adequate materials were used in manufacturing
• the determination as to whether a part design was adequate.
If the system that failed is well documented, then operational stresses can be calculated. For example, it can be determined how great the load was on a certain part when it failed. The load history may also be known throughout the time that the part was used. These data can be used to calculate the toughness, given a knowledge of the crack size at the time of final failure. This will show whether the part performed according to the specifications for it.
On the other hand, if the stresses are not known, then toughness still can be estimated from materials handbooks, again knowing the crack size and the area of the remaining sound metal at the time of failure.
If neither toughness nor stresses are known, toughness can be estimated from physical testing, using Charpy-impact tests on pieces of the material. The stresses at failure can be determined by back-calculation and it can then be said if the part failed from overload.
Much can be also done to quantify conditions from fatigue failures. The rate of crack-growth can be estimated from a knowledge of the number of striations per unit length of crack perpendicular to the crack front. If the stresses are known, the stress intensity can be inferred, and the adequacy of the material for the use conditions can be determined. From a knowledge of the known stresses, the crack size at fracture and the crack growth-rate, estimates may be made as to whether or not the material had been misused.
Thus, fracture mechanics can be used to help us understand
• how a particular crack formed at a specific location and
• the stress conditions that caused the crack to propagate.
The design engineer will normally include “factors of safety” in his design to prevent stresses from reaching critical levels .
More detailed examples of the applications of Fracture Mechanics to failure analysis are given in Appendix A.
11. Determine the type of failure
The major types of failures likely to be encountered by metals in service are:
B. Brittle, and
C. Fatigue fractures
Wear, Fretting, Elevated Temperature and Corrosion are other important causes of failure which will be covered in a future publication in this series.
A. Ductile Fracture
Ductile fractures are characterized by tearing of metal accompanied by appreciable gross plastic deformation. The microstructure of the fracture surface is quite complex and may include both transgranular and intergranular fracture mechanisms. Ductile fractures in most metals have a gray fibrous appearance and may be flat-faced (tensile overload) or slant-faced (shear). The specimen usually shows considerable elongation and possible reduction of cross-sectional area as well. Whether a part fails in a ductile or brittle fashion depends on the thickness of the part, temperature, strain rate and the presence of stress-raisers. Most commonly seen characteristics of ductile failures are:
• Lateral contraction, or necking;
• Fracture path in the interior following a generally flat plane perpendicular to the principal stress direction, and
• Tensile stress.
Cylindrical specimens will have a “cup and cone” configuration, as shown above on the right, while the fracture surface on thick specimens will be generally perpendicular to the principal stress direction, as seen in the bolt in the illustrations above.
B. Brittle Fracture
Brittle fractures are characterized by rapid crack propagation without appreciable plastic deformation. If brittle fractures occur across particular crystallographic planes they are called Tran crystalline fracture. If along grain boundaries they are called intergranular fracture. Brittle fracture is promoted by:
• thicker section sizes,
• lower service temperatures, and
• increased strain rate.
A material’s tendency to fracture in a brittle mode can be determined by measuring its notch ductility. The most common test for this is the Charpy V-notch test. Failure under test condition can exhibit energy and fracture transitions. Shear fracture occurs under the notch and along the free surfaces. Cleavage fracture occurs in the center characterized by a bright, shiny, faceted surface. 50% cleavage is the fracture transition point. Cleavage fracture is caused by inability of the crystal structure to cross-slip. Yield strength loading is required to initiate a brittle fracture; however, only much lower stress may be needed to propagate it. Generally speaking, body-centered cubic metals exhibit a ductile to brittle transition over a relatively narrow temperature range.
The Drop Weight Test defines the nil-ductility transition temperature and is very useful for determining the brittle fracture susceptibility of low-strength steels. Linear elastic fracture mechanics evaluates structural reliability in terms of applied stress, crack length and stress intensity at the crack tip.
C. Fatigue fracture
Fatigue is a progressive localized permanent structural change that occurs in a material subjected to repeated or fluctuating stresses well below the ultimate tensile strength (UTS). Fatigue fractures are caused by the simultaneous action of cyclic stress, tensile stress, and plastic strain, all three of which must be present. Cyclic stress initiates a crack and tensile stress propagates it. Final sudden failure of the remaining cross-section occurs by either shear or brittle fracture. Striations on the crack surface are the classic sign of fatigue fracture.
High Cycle Fatigue Low Cycle Fatigue Fatigue cracks may start because of tool marks, scratches, indentations, corrosion pits and areas of high stress. At the crack tip, the material is plastic. At a small distance from the crack tip, in the material is elastic.
Low cycle fatigue cracks occur under conditions of high strain amplitude (with failure in less than about 104 cycles) whereas high cycle fatigue occurs with low strain amplitude with failure after a large number of load fluctuations. In low cycle fatigue, striations, if visible at all, tend to be rather broad, widely spaced, and discontinuous in places. Areas without striations may appear to be rubbed or may be quite featureless, except for the area of final fracture. In high cycle fatigue, the striations will be well defined and more closely spaced, with propagation evident in many flat plateaus that are joined by narrow regions of tensile tearing. The investigator should be aware, however, that in heat-treated steels striations are absent from fatigue fractures more often than they are observed, and the stronger (harder) the steel, the less likely it is that striations will be observable. Thus, suspected fatigue striations must be studied carefully to ensure that they are not artifacts of some other process. Striations should be parallel to one another along their lengths and perpendicular to the fracture direction at the region being examined.
Thermal Fatigue cracking is caused by cycling the temperature of the part in the presence of mechanical constraint, e.g., rigid mounting of pipe. It could also be caused by temperature gradients in the part.
Contact Fatigue - Elements that roll, or roll and slide against each other under high contact pressure are subject to the development of surface pits or fatigue spalls after many repetitions of load.
Corrosion pit acting as stress concentrator for fatigue crack (on left at low magnification. Higher magnification of crack tip on right.
Corrosion-Fatigue is caused by the combined action of repeated or fluctuating stress and a corrosive environment to produce failure. It frequently initiates at a corrosion pit on the surface. A very aggressive environment may actually slow the fatigue fracture process increasing the number of stress cycles to failure. The environment affects the crack growth rate, or the probability of fatigue crack initiation, or both. Test data show that for high strength steels, the fatigue strength at 10 million cycles in salt water can be reduced to as little as 10% of that in dry air. Carbon steels exhibit transgranular fracture. Copper and its alloys fail by intergranular fracture.
12. Synthesize and summarize the data, determine and report the root-cause of the failure. Proposed root causes of a failure must be based primarily on observed facts. These facts, combined with the experience, skill and knowledge of the analyst will lead to sound conclusions.
All the observed data should be reported, even if some of it seems peripheral. In the future, with additional data, it may turn out to be possible to use what seemed peripheral at first to make an even more sound interpretation.