Fatigue des métaux
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Overview
Source : Roberto Leon, département de génie Civil et environnemental, Virginia Tech, Blacksburg, VA
L’importance d’étudier la fatigue du métal dans les projets d’infrastructure civile a été mis sous les projecteurs par l’effondrement du pont Silver au Point Pleasant, Virginie-occidentale en 1967. Le pont suspendu de chaînes eyebar au-dessus de la rivière Ohio s’est écroulé pendant l’heure de pointe du soir, tuant 46 morts à la suite de la défaillance d’un seul eyebar avec un petit défaut de 0,1 pouce. Le défaut a atteint une longueur critique après avoir répété les conditions de chargement et a échoué de façon fragile, causant l’effondrement. Cet événement a retenu l’attention de la communauté des ingénieurs pont et souligné l’importance de la vérification et la surveillance de fatigue en métal.
Dans des conditions normales de service, un matériau peut être soumis à de nombreuses applications des charges de service (ou tous les jours). Ces charges sont généralement au maximum 30 % – 40 % de la résistance à la rupture de la structure. Cependant, après l’accumulation de charges répétées, à magnitude sensiblement inférieure à la résistance à la rupture, un matériau peut éprouver ce qu’on appelle la rupture par fatigue. Rupture par fatigue peut survenir soudainement et sans déformation préalable significative et est liée avec craquelure et propagation rapide. La fatigue est un processus complexe, avec de nombreux facteurs qui affectent la résistance à la fatigue (tableau 1). Cette complexité souligne la nécessité intégrante d’inspection systématique et approfondie des structures soumises à des charges répétées telles que les ponts, les grues et presque tous les types de véhicules et des aéronefs.
| Soulignant les conditions | Propriétés des matériaux | Conditions environnementales |
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Le tableau 1. Facteurs qui influent sur la fatigue
Principles
Procedure
Results
The final results, in terms of stress range vs. number of cycles, should be tabulated (Table 2) and plotted, as demonstrated in Fig. 2. The actual yield stress of the specimen was 65.3 ksi and its tensile strength was 87.4 ksi so the stress ranges shown here correspond to between 23% and 92% of yield.
| Test | Area (in.2) | Inertia (in.4) | Length (in.) | Load (lbs) | Moment (lbs-in.) | Stress (psi) | Number of cycles (N) |
| 1 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 2.50E+00 | 1.91E+01 | 7.541E+01 | 1.00E+07 |
| 2 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 5.00E-01 | 3.82E+00 | 1.508E+01 | 8.95E+04 |
| 3 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 1.00E+00 | 7.64E+00 | 3.016E+01 | 1.20E+04 |
| 4 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 1.50E+00 | 1.15E+01 | 4.525E+01 | 7.80E+03 |
| 5 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 2.00E+00 | 1.53E+01 | 6.033E+01 | 1.23E+03 |
| 6 | 5.102E-03 | 5.102E-03 | 7.64E+00 | 2.50E+00 | 1.91E+01 | 7.541E+01 | 2.10E+02 |
Table 2. Typical results
The data shows that for a number of cycles less than about 100,000, there is a decreasing linear relationship between the stress range and the log of the number of cycles if the stress range exceeds 15 ksi. The best-fit line, then, indicates for a stress range of 25 ksi the number of cycles to failure is about 31,000. Below a stress range of 15 ksi, no failure is indicated. This is considered the endurance limit. The reliability of the endurance limit can be improved by testing more specimens between 10 ksi and 20 ksi.
Figure 2: Resulting S-N curve. Please click here to view a larger version of this figure.
If the cyclic load history of a bridge is assumed to consist of a number of cycles (Nexp) and stress ranges (SR) (Table 3), and we know the fatigue behavior of the material, we can use Miner's rule to calculate the cycles to failure by finding the Nmax from the graph in Fig. 2 and summing the Nexp/Nmax across all the stress ranges.
| SR (ksi) | Nexp | Nmax | Nexp /Nmax |
| 50 | 100 | 3431 | 0.029 |
| 45 | 200 | 5327 | 0.038 |
| 40 | 600 | 8272 | 0.073 |
| 35 | 2000 | 12843 | 0.156 |
| 30 | 5000 | 19942 | 0.251 |
| 25 | 6000 | 30964 | 0.194 |
| 20 | 10000 | 48078 | 0.208 |
| 15 | 1000000 | 100000000 | 0.010 |
| Sum = | 0.957 |
Table 3. Calculation for Miner's Rule
As expected, percentagewise, the higher stress ranges have a much larger impact on the damage accumulation. The structure seems to be near its design fatigue life capacity as the value is close to 1.0.
Applications and Summary
Fatigue failures are common in structures subjected to cyclic loads, such as bridges being loaded by heavy trucks. This failure type is due to the growth of preexisting small cracks in areas of large stress concentrations or multi-axial stresses. The initial crack growth is very slow but accelerates with time, eventually reaching a critical size after which the crack propagates at the speed of sound and failure occurs. The principal parameters governing fatigue behavior are the number of cycles and the stress range. In this test, a rotating beam machine was used to impose large number of alternating cycles of tension and compression to a small round beam. The results showed not only the typical trend of S-N curves, but also the significant scatter expected from a test of this type.
Studying fatigue failure helped airplane engineers understand the famous failure of the Comet Airliner. The DeHavilland Company built the Comet Airliner in 1952, making it the most advanced airliner at the time by halving the flight time from Tokyo to London. It flew at relatively high altitudes to achieve this speed, thus it was the first jet airliner to be pressurized. After three airlines exploded in flight in the short span of two years, engineers were charged with determining the source of the failure. To test the effect of normal conditions of use, they took the fuselage of the airliner and submerged it in a swimming pool to simulate pressurization and de-pressurization. The engineers determined that the failure was due to stress concentrations at the corners of the windows fatiguing over repeated loading conditions. As a result, modern day design of airplanes includes rounder corners to counteract this force and reduce the stress concentrations. While the DeHavilland Company was dealing with this safety issue, Boeing learned from this lesson in developing its Boeing 707 airliner, the first of a series of highly successful aircrafts. Boeing prospered and is now the leading manufacturer of airplanes around the world. Today, the successful development of any product that is subjected to large number of loading cycles requires extensive analytical and experimental work to characterize fatigue behavior, in addition to the implementation of a rigorous inspection plan that utilizes fault-tolerant design concepts.
Another example of fatigue failure occurred on the Brandywine River Bridge in 1997. A significant crack was recently discovered on this I-95 bridge over the Brandywine River in Delaware. The steel girder bridge carries six lanes of traffic just north of downtown Wilmington. The crack was located on the fascia girder at mid-span of the bridge’s main span. The entire bottom flange was fractured, with the crack extending upwards to within 0.3 meters of the upper flange. In this case, a jogger on the trail below alerted authorities after seeing evidence of the failure. Since the fascia girder is lightly loaded and the bridge had many additional girders (i.e., exhibited redundancy in its load paths), a catastrophic failure was luckily avoided.
Transcript
Fatigue failure in metal structures that undergo cyclic loading can occur without warning at loads significantly below the ultimate strength of a structure. It is difficult to model this behavior, so it is important to assess fatigue characteristics in the laboratory and to monitor fatigue cracks in the field.
The collapse of the Silver Bridge over the Ohio River brought the importance of metal fatigue to the attention of the engineering community in 1967. The bridge failed in a brittle fashion due to corrosion fatigue, killing 46 people. The fatigue failure occurred in an eyebar connection not visible to inspectors, and was probably due to a manufacturing flaw.
Fatigue failure can happen as materials experience many cycles of loads at stresses that may only be 30 to 40% of their ultimate strength. Crack growth and propagation during this type of cyclic loading can result in sudden fatigue failure with few warning signs. Fatigue is a complex process with many factors effecting fatigue resistance.
High cycle, low stress range conditions occur in equipment or structures with moving parts or loads, like cars on bridges or rotating machinery in a manufacturing plant. Low cycle, high stress range fatigue occurs in situations such as earthquakes.
This video will illustrate the need for laboratory testing of materials and monitoring of structures subjected to repeated low stress, high cycle loading to avoid catastrophic fatigue failures.
A fatigue crack usually initiates at an angle to the normal stress, but then turns and grows perpendicular to the principle tensile stress. The crack propagates under tensile, or sheer stress, but not under compressive stress.
After repeated loading, the crack reaches a critical length and it suddenly propagates at the speed of sound, leading to immediate failure. The initial crack growth produces characteristic beach marks on the fatigue fracture surface. A rougher fracture surface is produced on the material surface that fails suddenly.
Fatigue failure is defined by the number of cycles and the stress range to failure. As the applied stress range increases, the number of cycles to failure decreases. Most metals and ferrous alloys have an endurance limit below which they will not fail regardless of the number of cycles. The cycles at a particular stress range is random in real life cyclic loading. Because of this, there is more than one stress range and more than one corresponding number representing cycles to failure.
Miner’s rule is used by defining a set of stress ranges and grouping cycles into these ranges. The number of loading cycles expected is divided by cycles to failure for each stress range and summed. If the sum is greater than 1, fatigue failure is possible. Although there is no physical basis for this equation, it is useful for engineering design purposes. A large number of stress ranges and cycles to failure can be tested using a rotating beam test.
In this test, a cantilever bending configuration is used while the specimen is rotated. The load to be applied is determined using the yield strength to calculate a set of stress ranges. For example, a typical structural steel has a yield strength of 50 ksi, and the calculation for the first stress range of plus or minus 15% gives a load of plus or minus 7.5 ksi. This load is applied and the specimen experiences full tension and full compression during each revolution.
An S-N curve is produced relating the stress range to the log value of the number of cycles to failure. In the next section, we will test steel specimens using a more rotating beam machine to produce an S-N curve for the material.
Obtain five A572 grade specimens to be tested using a rotating cantilever setup on a Moore rotating beam machine. The dimensions of the specimens used and the distances to the loading points are particular to the testing machine being used.
These dimensions may vary with your own test setup. Our specimens are 2.40 inches in length and 0.15 inches in diameter. The small necked section of each specimen is 0.50 inches in length and 0.04 inches in diameter.
Mount the first specimen in the machine with the necked section near the middle of the beam. Measure the distance from the center of the specimen to the load point. Carefully align the specimens so that the beam rotates freely and without wobbling, and then apply a load at the cantilever end. The cantilever specimen is loaded at the tip by using a point load generated by a set of springs and whose value is monitored by a load cell. The load is applied through a bearing so that the force is always downwards as the beam rotates.
The machine speed is set at 1400 rpms, the cycle counter is set to 0, and the test is started. The speed, specimen size, and applied stress will vary with the testing machine. Wait until the specimen fails and record the number of cycles to failure. Remove the failed specimen from the test machine and inspect its fracture surfaces.
Repeat, testing one specimen at each of the stress ranges to be tested. Many more specimens would need to be tested at each stress range to obtain statistically valid data.
Tabulate stress ranges and number of cycles and plot the results. The actual yield stress of the specimen was 65.3 ksi, and its tensile strength was 87.4 ksi. Stress ranges shown here correspond to between 23% and 92% of yield.
The data shows that for a stress range above 15 ksi and cycles less than 100,000, there is a decrease in linear relationship between the stress range and the log of the number of cycles. The best fit line then indicates for a stress range of 25 ksi, the number of cycles to failure is about 31,000.
Below a stress range of 15 ksi, no failure is indicated. This is considered the endurance limit. The reliability of the endurance limit can be improved by testing more specimens between 10 ksi and 20 ksi.
If the cyclic load history of a bridge is assumed to consist of a number of cycles and stress ranges, and we know the fatigue behavior of the material, we can use Miner’s rule to calculate the cycles to failure.
As expected, percentage wise, the higher stress ranges have a much larger impact on the damage accumulation. The structure seems to be near its design fatigue life capacity as the value is close to 1.0.
Now that you appreciate the roles of cyclic loading, testing, and monitoring in fatigue failure, let’s take a look at examples of how fatigue effects structures that we use everyday.
Bridges experience cyclic loading daily. A catastrophic failure was luckily avoided on the Brandywine River bridge in Wilmington Delaware. A significant crack discovered by a jogger on the trail below in 1997 was found propagating from a wield defect. Repairs have been made and the bridge continues to carry 6 lanes of traffic while being monitored in its use.
Engineers submerged fuselage in a swimming pool to simulate pressurization and depressurization after 3 airplanes exploded in flight in the 1950s. It was determined that after repeated loading due to stress concentrations at the corners of the windows, fatigue failure occurred. As a result, modern day design of airplanes includes rounder corners to counteract this force and reduce the stress concentrations.
You have just watched JoVE’s Introduction to the Fatigue of Metals. You should now understand the idea of cyclic loading and its effect on fatigue failure of metals.
Thanks for watching!