Why fracture mechanics

Many flaws are serious enough that they should be treated as cracks, and these include deep scratches, inclusions of foreign particles, and grain boundaries. In addition to material flaws, geometric features in a part which act as stress concentrations can lead to crack initiation, including notches, holes, grooves, and threads. Cracks can also initiate from flaws introduced through other failure mechanisms, such as from pitting due to corrosion or from abrasion due to galling. Determining the initial size of the crack is critical to assessing the potential for fracture.

A conservative approach is to select a non-destructive evaluation NDE method for inspecting the part under consideration, and then to assume that a crack equal in size to the minimum detectable flaw size exists in the part in the most highly stressed location. If the minimum detectable flaw size is unknown, or if an NDE inspection is not planned for the part, then an alternate approach is to determine the critical crack size at the most highly stressed location in the part.

If this critical crack size is very small, then it would be wise to inspect the part using an NDE method capable of detecting a crack of this size. The size of the plastic zone is dependent on whether the part is considered to be in a plane-stress or a plane-strain condition. In plane-stress, the section is thin enough that the stresses through the thickness of the section are approximately constant. In plane-strain, stresses develop through the thickness of the section to resist contraction of the material and to keep the strain throughout the thickness approximately constant.

The part can be considered to be in plane-strain if the thickness satisfies the following condition:. If the part thickness is less than that specified in the equation above, then the plastic zone size should be calculated assuming that the part is in plane-stress.

The table below summarizes the plastic zone sizes for plane-stress and plane-strain. Due to the sharp nature of the crack, there will always be a plastic zone just ahead of the crack tip. We can use the elastic stress field equations discussed in a previous section to solve for the theoretical distance from the crack tip at which the stresses are equal to the material's yield strength.

The elastic stress field equation is:. Setting the stress equal to the material's yield strength and solving for r gives the theoretical size of the plastic zone, r t :.

For the actual plastic zone size to be equal to the theoretical plastic zone size, the stresses in the plastic zone must substantially exceed the material's yield strength. Because the yielded material in the plastic zone cannot support stresses much above the yield stress, the stresses near the crack tip are redistributed to the material farther out, and therefore the true size of the plastic zone is larger than the theoretical predicted value.

The actual size of the plastic zone is approximately equal to 2r t , so a more realistic estimate of the plastic zone size, r p , is given by:. The figure below illustrates the theoretical elastic stress and plastic zone size, as well as the redistributed stresses and the resulting realistic estimate of the plastic zone size.

This indicates that the plastic zone will be smaller for higher strength materials. Additionally, higher toughness materials are able to develop higher stress intensities before fracture, so the plastic zone will grow larger in higher toughness materials before failure occurs.

Materials with low tensile strength and high fracture toughness can develop very large plastic zones at the crack tip. The plastic zone size estimates described in the previous section apply to the plane-stress condition where the section is thin enough that the stresses through the thickness of the section are approximately constant.

If the section is thick enough to be considered in plane-strain i. There are two frames of reference when discussing ductile fracture versus brittle fracture. These frames of reference are the fracture mechanism and the fracture mode. When materials scientists talk about brittle fracture and ductile fracture, they are typically referring to the fracture mechanism , which describes the fracture event at a microscopic level.

In general, the brittle fracture mechanism is cleavage , and the ductile fracture mechanism is dimpled rupture , also known as microvoid coalescence. The cleavage mechanism is associated with brittle fracture. It involves little plastic deformation, and the fracture surface looks smooth with ridges. The microvoid coalescence mechanism is associated with ductile fracture.

This mechanism involves the formation, growth, and joining of small voids in the material which is enabled through plastic flow, and the fracture surface looks dimpled like a golf ball.

When mechanical engineers talk about brittle fracture and ductile fracture, they are typically referring to the fracture mode , which describes the high-level behavior of the material during the fracture event.

The figure below illustrates the fracture mode. A load-displacement curve is shown along with cracked specimens placed at various locations along the curve. In the linear region of the curve with lower applied load, the stresses in the part are below the material yield strength. If the part were to fail in this region, this would be referred to as brittle fracture since the part has failed prior to what is predicted using strength-of-materials methods.

Note that in this region, the plastic zone around the crack tip shown in red will typically be small, and so the linear elastic assumption applies and Linear Elastic Fracture Mechanics LEFM can be used to analyze the part.

As the load increases, the plastic zone size increases. If the part fails in the higher region of the load-displacement curve, this is referred to as ductile fracture. If the plastic zone size has exceeded the applicability of LEFM but has not yet extended across the entire section, then elastic-plastic methods such as the Failure Assessment Diagram FAD can be used to analyze the part.

Once the plastic zone size has extended across the entire section gross section yielding , fracture mechanics methods can no longer be used, and the section will need to be analyzed using a strength-of-materials approach.

Static fracture analysis should be performed considering the peak load that the part is expected to see during its lifetime. In the static analysis methods, the load is steady and does not vary with time. On the other hand, fatigue crack growth analysis can be used to consider crack growth due to a time-varying load. The loads over the entire service life of the part are typically considered to ensure that the crack will not grow to a critical size.

The following sections describe several standard methods for performing static fracture analysis. The topic of fatigue crack growth is covered on another page. Linear elastic fracture mechanics LEFM uses the concept of the stress intensity factor , K , discussed previously.

The stress intensity factor at the crack tip is calculated and then compared to the critical stress intensity of the material. The plane-strain fracture toughness , K IC , is typically chosen as the value of critical stress intensity to use for design and analysis. The factor of safety is then calculated as:. Linear elastic fracture mechanics LEFM assumes that the material is behaving in a linear-elastic manner. For this assumption to be valid, the size of the plastic zone must be small relative to the part and crack geometry.

If the plastic zone size extends too close to the bounds of the part, then the situation approaches gross yielding of the section. The plastic zone is situated just ahead of the crack tip. Note that d LEFM is equal to 4 times the plastic zone size for the plane-stress condition. As an example, consider the case of a single-edge crack. In this case, the following condition must be met for LEFM to be applicable:. If LEFM is not applicable, then elastic-plastic analysis should be used to account for the effects of plasticity in the vicinity of the crack.

In the FAD diagram above, the failure locus is shown in red. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials.

It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Fracture mechanics is an important tool in improving the mechanical performance of components. It applies to the microscopic crystallographic defects found in materials in order to predict the macroscopic mechanical failure of bodies.

Fractography is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real-life failures.

Interior and surface flaws arising from the manufacturing process are found in all metal structures. Not all such flaws are unstable under service conditions. Fracture mechanics analyzes flaws to determine which are safe and which are liable to propagate as cracks and cause failure of the flawed structure. Fracture mechanics can estimate the maximum crack that a material can withstand before it fails, taking into consideration:.

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By: Della Anggabrata. Dictionary Dictionary Term of the Day. Corrosionpedia Terms. Anodize This: The Brilliance of Anodizing. Because cast steel was a new material to the design engineers, it was necessary to devise, in collaboration with the constructional engineers, new methods for testing and inspection.

Ultrasonic testing of the nodes for the main girders is shown in progress in the production stage. It was appreciated that some defects were inevitable in cast and welded components and that non-destructive tests could not be relied upon to reveal every shortcoming.

The fracture toughness tests showed the cast steel exhibited the required standards of quality. After preliminary welding tests had indicated the correct welding procedures, ultimate tests to collapse proved that it was possible to attain satisfactory and, in some cases, excellent results.

Enter a phrase to search for:. Search by. Full text Keywords. Headings Abstracts. Total Materia Extended Range includes the largest database of fracture mechanics parameters for hundreds of metal alloys and heat treatments conditions.

K1C, KC, crack growth and Paris law parameters are given, with the corresponding graph of crack growth. Monotonic properties are added for the reference, as well as estimates of missing parameters based on monotonic properties where applicable. Enter the material of interest into the quick search field. After clicking the material from the resulting list, a list of subgroups that are standard specifications appears.

Because Total Materia Extended Range fracture mechanics parameters are neutral to standard specifications, you can review fracture mechanics data by clicking the appropriate link for any of the subgroups. The data are given in a tabular format, with the Paris curve Region II where applicable.

Explicit references to the data sources are given for each dataset. Release Material Console provides multiple functionalities to support more efficient, accurate and personalized material selection decisions.

Total Materia remains the only tool which will be used for this purpose. Application of Fracture Mechanics Abstract: Fracture mechanics is a useful method of characterizing fracture toughness, fatigue crack growth, or stress-corrosion crack growth behavior in terms of structural design parameters familiar to the engineer, namely stress and flaw size.

Stress Intensity Range An example of the practical application to design may be given in the main structural framework of the Beaubourg Centre, Paris, France. Date Published: Sep Search Knowledge Base Enter a phrase to search for:.