Stress Concentration Crack Tip
A stress concentration often called stress raisers or stress risers is a location in an object where stress is concentrated. An object is strongest when force is.
Stress concentration is defined as - Localized stress considerably higher than average even in uniformly loaded cross sections of uniform thickness due to abrupt.
Stress Concentration Considerations. It is important to remember that stress amplification not only occurs on a microscopic level e.g. small flaws or cracks, but.
Beach Marks - Also known as clam shell marks. Beachmarks represent the propagation of a crack through a material due to fatigue. These marks are visible to the eye.
The fracture of a material is dependent upon the forces that exist
between the atoms. Because of the forces that exist between the
atoms, there is a theoretical strength that is typically estimated
to be one-tenth of the elastic modulus of the material. However,
the experimentally measured fracture strengths of materials are
found to be 10 to 1000 times below this theoretical value. The
discrepancy is explained to exist because of the presence of small
flaws or cracks found either on the surface or within the material.
These flaws cause the stress surrounding the flaw to be amplified
where the magnification is dependent upon the orientation and
geometry of the flaw. Looking at fig. 1, one can see a stress
profile across a cross section containing an internal, elliptically-shaped
crack. One can see that the stress is at a maximum at the crack
tip and decreased to the nominal applied stress with increasing
distance away from the crack. The stress is concentrated around
the crack tip or flaw developing the concept of stress concentration.
Stress raisers are defined as the flaws having the ability
to amplify an applied stress in the locale.
Fig. 1: a The geometry of surface and internal cracks.
b Schematic stress profile along the line X-X in a, demonstrating
stress amplification at crack tip positions.
Determination of the Maximum Stress at the Crack Tip
If the crack is assumed to have an elliptical shape and is oriented
with its long axis perpendicular to the applied stress, the maximum
approximated at the crack tip by Equation 1.
Eqn. 1: Determination of the maximum stress surrounding
The magnitude of the nominal applied tensile stress is so;
the radius of the curvature of the crack tip is r;
and a represents the length of a surface crack, or half
the length of an internal crack.
Determination of Stress Concentration Factor
The ratio of the maximum stress and the nominal applied tensile
stress is denoted as the stress concentration factor, Kt,
where Kt can be calculated by Equation 2. The
stress concentration factor is a simple measure of the degree
to which an external stress is amplified at the tip of a small
Eqn. 2: Determination of the stress concentration factor.
Stress Concentration Considerations
It is important to remember that stress amplification not only
occurs on a microscopic level e.g. small flaws or cracks, but
can also occur on the macroscopic level in the case of sharp
corners, holes, fillets, and notches. Fig. 2 depicts the theoretical
stress concentration factor curves for several simple and common
Fig. 2: Stress concentration factor plots for three different
Stress raisers are typically more destructive in brittle materials.
Ductile materials have the ability to plastically deform in the
region surrounding the stress raisers which in turn evenly distributes
the stress load around the flaw. The maximum stress concentration
factor results in a value less than that found for the theoretical
value. Since brittle materials cannot plastically deform, the
stress raisers will create the theoretical stress concentration
Callister, William D. Materials Science and Engineering:
An Introduction - 3rd Edition. John Wiley
Virginia Tech Materials Science and Engineering
Stress corrosion cracking SCC is the growth of crack formation in a corrosive environment. It can lead to unexpected sudden failure of normally ductile metals.
Structural Integrity Analysis 1. Stress Concentration Copyrighted materials.
Internal force lines are denser near the hole
A stress concentration often called stress raisers or stress risers is a location in an object where stress is concentrated. An object is strongest when force is evenly distributed over its area, so a reduction in area, e.g., caused by a crack, results in a localized increase in stress. A material can fail, via a propagating crack, when a concentrated stress exceeds the material s theoretical cohesive strength. The real fracture strength of a material is always lower than the theoretical value because most materials contain small cracks or contaminants especially foreign particles that concentrate stress. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue strength.
4 Concentration factor for cracks
5 Concentration factor calculation
The sharp corner at the brick has acted as a stress concentrator within the concrete causing it to crack
Geometric discontinuities cause an object to experience a local increase in the intensity of a stress field. Examples of shapes that cause these concentrations are cracks, sharp corners, holes, and changes in the cross-sectional area of the object. High local stresses can cause objects to fail more quickly, so engineers must design the geometry to minimize stress concentrations.
A counter-intuitive method of reducing one of the worst types of stress concentrations, a crack, is to drill a large hole at the end of the crack. citation needed The drilled hole, with its relatively large diameter, causes a smaller stress concentration than the sharp end of a crack. citation needed This is however, a temporary solution that must be corrected at the first opportune time. citation needed
It is important to systematically check for possible stress concentrations caused by cracks there is a critical crack length of 2a for which, when this value is exceeded, the crack proceeds to definite catastrophic failure. This ultimate failure is definite since the crack will propagate on its own once the length is greater than 2a. There is no additional energy required to increase the crack length so the crack will continue to enlarge until the material fails. The origins of the value 2a can be understood through Griffith s theory of brittle fracture.
Another method used to decrease the stress concentration is by creating the fillet at the sharp edges. It gives smooth flow of stress streamlines. In a threaded component force flow line is bent as it passes from shank portion to threaded portion as a result stress concentration takes place. To reduce this a small undercut is taken between shank and threaded portion.
This orthosis is implanted to support the femur after a fracture, but the concentration of stress at its bend increases the possibility that it may break under force.
The term stress raiser is used in orthopedics; a focus point of stress on an implanted orthosis is very likely to be its point of failure.
Classic cases of metal failures due to stress concentrations include metal fatigue at the corners of the windows of the De Havilland Comet aircraft and brittle fractures at the corners of hatches in Liberty ships in cold and stressful conditions in winter storms in the Atlantic Ocean.
Concentration factor for cracks edit
The maximum stress felt near a crack occurs in the area of lowest radius of curvature. In an elliptical crack of length and width, under an applied external stress, the stress at the ends of the major axes is given by:
where ρ is the radius of curvature of the crack tip. A stress concentration factor is the ratio of the highest stress to a reference stress of the gross cross-section. As the radius of curvature approaches zero, the maximum stress approaches infinity. Note that the stress concentration factor is a function of the geometry of a crack, and not of its size. These factors can be found in typical engineering reference materials to predict the stresses that could otherwise not be analyzed using strength of materials approaches. This is not to be confused with Stress Intensity Factor. 1
Concentration factor calculation edit
There are experimental methods for measuring stress concentration factors including photoelastic stress analysis, brittle coatings or strain gauges. While all these approaches have been successful, all also have experimental, environmental, accuracy and/or measurement disadvantages.
During the design phase, there are multiple approaches to estimating stress concentration factors. Several catalogs of stress concentration factors have been published. Perhaps most famous is Stress Concentration Design Factors by Peterson, first published in 1953. 2 Finite element methods are commonly used in design today. Theoretical approaches, using elasticity or strength of material considerations, can lead to equations similar to the one shown above.
There may be small differences between the catalog, FEM and theoretical values calculated. Each method has advantages and disadvantages. Many catalog curves were derived from experimental data. FEM calculates the peak stresses directly and nominal stresses may be easily found by integrating stresses in the surrounding material. The result is that engineering judgment may have to be used when selecting which data applies to making a design decision. Many theoretical stress concentration factors have been derived for infinite or semi-infinite geometries which may not be analyzable and are not testable in a stress lab, but tackling a problem using two or more of these approaches will allow an engineer to achieve an accurate conclusion.
Schijve, Jaap 2001. Fatigue of Structures and Materials. Springer. p. 90. ISBN 978-0792370147.
Peterson, Rudolf Earl 1953. Stress Concentration Design Factors. John Wiley Sons. ISBN 978-0471683766.
ESDU64001: Guide to stress concentration data ISBN 1-86246-279-8
Pilkey, Walter D, Peterson s Stress Concentration Factors, Wiley, 2nd Ed 1999. ISBN 0-471-53849-3
Structural Integrity Analysis: Stress Concentration
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Categories: Engineering conceptsElasticity physics Orthopedic surgical procedures.
The effect of notches on multiaxial fatigue behavior was studied using thin-walled tubular 2024-T3 aluminum specimens with a circular transverse hole. Constant.
