40:
1068:
impurities dislocations in the material. To move this defect (plastically deforming or yielding the material), a larger stress must be applied. This thus causes a higher yield stress in the material. While many material properties depend only on the composition of the bulk material, yield strength is extremely sensitive to the materials processing as well.
1067:
There are several ways in which crystalline materials can be engineered to increase their yield strength. By altering dislocation density, impurity levels, grain size (in crystalline materials), the yield strength of the material can be fine-tuned. This occurs typically by introducing defects such as
1877:
That experimentally measured yield strength is significantly lower than the expected theoretical value can be explained by the presence of dislocations and defects in the materials. Indeed, whiskers with perfect single crystal structure and defect-free surfaces have been shown to demonstrate yield
1054:
correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another. Hardness testing can therefore be an economical substitute for tensile testing, as well as providing local variations in yield strength due
891:
Beyond the elastic limit, permanent deformation will occur. The elastic limit is, therefore, the lowest stress point at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on the equipment used and operator skill. For
1413:
Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocations within the crystal. A line defect that, while moving through the matrix, will be forced against a small particle or precipitate of the material. Dislocations can move through this particle
2359:
When these conditions are undesirable, it is essential for suppliers to be informed to provide appropriate materials. The presence of YPE is influenced by chemical composition and mill processing methods such as skin passing or temper rolling, which temporarily eliminate YPE and improve surface
1881:
The theoretical yield strength can be estimated by considering the process of yield at the atomic level. In a perfect crystal, shearing results in the displacement of an entire plane of atoms by one interatomic separation distance, b, relative to the plane below. In order for the atoms to move,
1647:
Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Since it requires a lot of energy to move dislocations to
2347:
Yield Point
Elongation (YPE) significantly impacts the usability of steel. In the context of tensile testing and the engineering stress-strain curve, the Yield Point is the initial stress level, below the maximum stress, at which an increase in strain occurs without an increase in stress. This
2355:
YPE can lead to issues such as coil breaks, edge breaks, fluting, stretcher strain, and reel kinks or creases, which can affect both aesthetics and flatness. Coil and edge breaks may occur during either initial or subsequent customer processing, while fluting and stretcher strain arise during
1034:
Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. The structure will be permanently deformed when the load is removed, and may have residual stresses. Engineering metals display strain hardening, which implies that the yield stress is
1055:
to, e.g., welding or forming operations. For critical situations, tension testing is often done to eliminate ambiguity. However, it is possible to obtain stress-strain curves from indentation-based procedures, provided certain conditions are met. These procedures are grouped under the term
1021:, reach an upper yield point before dropping rapidly to a lower yield point. The material response is linear up until the upper yield point, but the lower yield point is used in structural engineering as a conservative value. If a metal is only stressed to the upper yield point, and beyond,
1223:
the material, impurity atoms in low concentrations will occupy a lattice position directly below a dislocation, such as directly below an extra half plane defect. This relieves a tensile strain directly below the dislocation by filling that empty lattice space with the impurity atom.
2112:
1882:
considerable force must be applied to overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site. The applied stress to overcome the resistance of a perfect lattice to shear is the theoretical yield strength, τ
1478:
1105:, which increases their density in the material. This increases the yield strength of the material since now more stress must be applied to move these dislocations through a crystal lattice. Dislocations can also interact with each other, becoming entangled.
1550:
2192:
1878:
stress approaching the theoretical value. For example, nanowhiskers of copper were shown to undergo brittle fracture at 1 GPa, a value much higher than the strength of bulk copper and approaching the theoretical value.
1955:
1289:
2343:
exhibit a distinct upper yield point or a delay in work hardening. These tensile testing phenomena, wherein the strain increases but stress does not increase as expected, are two types of yield point elongation.
1043:
Yield strength testing involves taking a small sample with a fixed cross-section area and then pulling it with a controlled, gradually increasing force until the sample changes shape or breaks. This is called a
1011:
is multiplied by a factor of safety to obtain a lower value of the offset yield point. High strength steel and aluminum alloys do not exhibit a yield point, so this offset yield point is used on these materials.
1986:
1716:
1648:
another grain, these dislocations build up along the boundary, and increase the yield stress of the material. Also known as Hall-Petch strengthening, this type of strengthening is governed by the formula:
1155:
421:
2282:
1609:
1889:
The stress displacement curve of a plane of atoms varies sinusoidally as stress peaks when an atom is forced over the atom below and then falls as the atom slides into the next lattice point.
1423:
1637:
1581:
982:
949:
2326:
896:, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses.
1009:
355:, which is the load-bearing capacity for a given material. The ratio of yield strength to ultimate tensile strength is an important parameter for applications such steel for
1980:
is the interatomic separation distance. Since τ = G γ and dτ/dγ = G at small strains (i.e. Single atomic distance displacements), this equation becomes:
2222:
313:
and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable
1749:
1185:
1403:
100:
76:
2348:
characteristic is typical of certain materials, indicating the presence of YPE. The mechanism for YPE has been related to carbon diffusion, and more specifically to
1383:
1312:
1209:
1978:
1793:
1771:
1356:
1336:
317:
in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as
1489:
249:
2558:
2811:
2123:
2422:"Automated Calculation of Strain Hardening Parameters from Tensile Stress vs. Strain Data for Low Carbon Steel Exhibiting Yield Point Elongation"
1414:
either by shearing the particle or by a process known as bowing or ringing, in which a new ring of dislocations is created around the particle.
1895:
2887:
1233:
2494:
2107:{\displaystyle G={\frac {d\tau }{dx}}={\frac {2\pi }{b}}\tau _{\max }\cos \left({\frac {2\pi x}{b}}\right)={\frac {2\pi }{b}}\tau _{\max }}
918:
is arbitrarily defined. The value for this is commonly set at 0.1% or 0.2% plastic strain. The offset value is given as a subscript, e.g.,
3080:
2459:
1654:
700:
294:
is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as
871:
move. This definition is rarely used since dislocations move at very low stresses, and detecting such movement is very difficult.
1874:
The theoretical yield strength of a perfect crystal is much higher than the observed stress at the initiation of plastic flow.
242:
2589:
3071:
3038:
3002:
2968:
2946:
2925:
2638:
1114:
328:, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield point (or
373:
295:
287:
2234:
1586:
2787:
3056:
3021:
2987:
235:
2532:
1473:{\displaystyle \Delta \tau ={\frac {r_{\text{particle}}}{l_{\text{interparticle}}}}\gamma _{\text{particle-matrix}}}
3115:
2385:
2117:
For small displacement of γ=x/a, where a is the spacing of atoms on the slip plane, this can be rewritten as:
2825:
Richter, Gunther (2009). "Ultrahigh
Strength Single-Crystalline Nanowhiskers Grown by Physical Vapor Deposition".
1614:
2360:
quality. However, YPE can return over time due to aging, which is holding at a temperature usually 200-400 °C.
2356:
forming. Reel kinks, transverse ridges on successive inner wraps of a coil, are caused by the coiling process.
17:
3105:
3095:
2337:
3120:
2565:
1558:
1090:
1080:
902:
The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur.
310:
1085:
954:
921:
198:
2290:
188:
2390:
987:
533:
360:
352:
203:
2847:
3110:
2200:
1727:
1163:
1056:
914:
When a yield point is not easily defined on the basis of the shape of the stress-strain curve an
857:
208:
43:
31:
2498:
2842:
2368:
1388:
178:
85:
860:
exhibited by real materials. In addition, there are several possible ways to define yielding:
2630:
2624:
2395:
1048:
Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers.
112:
61:
2463:
2834:
2739:
2380:
1361:
1297:
1194:
1051:
337:
283:
279:
8:
2349:
370:, the yield point can be specified in terms of the three-dimensional principal stresses (
332:) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual
275:
193:
158:
2838:
2743:
1545:{\displaystyle \Delta \tau ={\frac {Gb}{l_{\text{interparticle}}-2r_{\text{particle}}}}}
881:), so the stress-strain graph is a straight line, and the gradient will be equal to the
3100:
2805:
2757:
1963:
1778:
1756:
1341:
1321:
291:
183:
163:
107:
79:
55:
2667:
3067:
3052:
3034:
3017:
2998:
2983:
2964:
2942:
2935:
Avallone, Eugene A.; Baumeister, Theodore; Sadegh, Ali; Marks, Lionel Simeon (2006).
2921:
2860:
2793:
2783:
2761:
2654:
Barnes, Howard (1999). "The yield stress—a review or 'παντα ρει'—everything flows?".
2634:
2441:
263:
153:
51:
2852:
2747:
2663:
2433:
341:
3028:
2958:
2936:
1045:
882:
599:
560:
367:
314:
2600:
A. M. Howatson, P. G. Lund and J. D. Todd, "Engineering Tables and Data", p. 41.
2437:
1188:
1187:
is the yield stress, G is the shear elastic modulus, b is the magnitude of the
1075:
878:
585:
123:
30:
This article is about the science of material yield. For predicting yield, see
2752:
2727:
2363:
Despite its drawbacks, YPE offers advantages in certain applications, such as
1022:
856:
It is often difficult to precisely define yielding due to the wide variety of
3089:
2797:
2728:"Correlation of Yield Strength and Tensile Strength with Hardness for Steels"
2536:
2445:
2421:
2400:
2187:{\displaystyle G={\frac {d\tau }{d\gamma }}={\frac {2\pi a}{b}}\tau _{\max }}
547:
424:
333:
213:
117:
2915:
2864:
2364:
1315:
520:
431:. A variety of yield criteria have been developed for different materials.
1102:
868:
651:
624:
322:
267:
1950:{\displaystyle \tau =\tau _{\max }\sin \left({\frac {2\pi x}{b}}\right)}
1018:
507:
483:
2856:
2420:
Scales, M.; Kornuta, J.A.; Switzner, N.; Veloo, P. (1 December 2023).
1284:{\displaystyle \Delta \tau =Gb{\sqrt {C_{s}}}\epsilon ^{\frac {3}{2}}}
893:
574:
458:
348:
318:
148:
3061:
841:
827:
799:
664:
356:
173:
143:
2957:
Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John T. (2001).
1405:
is the strain induced in the lattice due to adding the impurity.
785:
168:
877:
Up to this amount of stress, stress is proportional to strain (
771:
686:
682:
678:
1711:{\displaystyle \sigma _{y}=\sigma _{0}+kd^{-{\frac {1}{2}}}\,}
39:
2978:
Boresi, A. P., Schmidt, R. J., and
Sidebottom, O. M. (1993).
2934:
2340:
1220:
638:
351:
materials, the yield strength is typically distinct from the
325:
1611:
is the surface tension between the matrix and the particle,
2916:
Avallone, Eugene A. & Baumeister III, Theodore (1996).
713:
218:
2419:
2993:
Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003).
813:
2941:(11th, Illustrated ed.). McGraw-Hill Professional.
290:
and will return to its original shape when the applied
2336:
During monotonic tensile testing, some metals such as
2287:
The theoretical yield strength can be approximated as
2293:
2237:
2203:
2126:
1989:
1966:
1898:
1781:
1759:
1730:
1657:
1617:
1589:
1561:
1492:
1426:
1408:
1391:
1364:
1344:
1324:
1300:
1236:
1197:
1166:
1117:
990:
957:
924:
376:
88:
64:
2622:
1150:{\displaystyle \Delta \sigma _{y}=Gb{\sqrt {\rho }}}
3064:
Roark's
Formulas for Stress and Strain, 7th edition
3062:Young, Warren C. & Budynas, Richard G. (2002).
3012:Oberg, E., Jones, F. D., and Horton, H. L. (1984).
1071:These mechanisms for crystalline materials include
416:{\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}}
2992:
2956:
2519:
2320:
2277:{\displaystyle \tau _{\max }={\frac {Gb}{2\pi a}}}
2276:
2216:
2186:
2106:
1972:
1949:
1787:
1765:
1743:
1710:
1631:
1604:{\displaystyle \gamma _{\text{particle-matrix}}\,}
1603:
1575:
1544:
1472:
1397:
1377:
1350:
1330:
1306:
1283:
1203:
1179:
1149:
1029:
1003:
976:
943:
415:
94:
70:
27:Phenomenon of deformation due to structural stress
2938:Mark's Standard Handbook for Mechanical Engineers
2918:Mark's Standard Handbook for Mechanical Engineers
286:behavior. Below the yield point, a material will
3087:
2732:Journal of Materials Engineering and Performance
2371:. Generally, steel with YPE is highly formable.
2299:
2243:
2209:
2179:
2099:
2039:
1910:
2725:
2331:
1642:
1214:
359:, and has been found to be proportional to the
2888:"Yield Point Elongation (YPE) – Pros and Cons"
1035:increased after unloading from a yield state.
1799:
1108:The governing formula for this mechanism is:
243:
2810:: CS1 maint: multiple names: authors list (
2629:. Boston: Houghton Mifflin Company. p.
2626:Engineering Materials and their Applications
1751:is the stress required to move dislocations,
1227:The relationship of this mechanism goes as:
1101:Where deforming the material will introduce
3047:Shigley, J. E., and Mischke, C. R. (1989).
2623:Flinn, Richard A.; Trojan, Paul K. (1975).
1062:
2773:
2771:
1632:{\displaystyle l_{\text{interparticle}}\,}
984:MPa. For most practical engineering uses,
250:
236:
2846:
2751:
2691:
2689:
1707:
1628:
1600:
1572:
2995:Materials and Processes in Manufacturing
2656:Journal of Non-Newtonian Fluid Mechanics
2647:
38:
2920:(8th ed.). New York: McGraw-Hill.
2824:
2768:
1639:is the distance between the particles.
14:
3088:
2726:Pavlina, E.J.; Van Tyne, C.J. (2008).
2686:
2653:
2603:
2533:"Technical Product Data Sheets UHMWPE"
1358:are the same as in the above example,
2982:, 5th edition John Wiley & Sons.
2882:
2880:
2878:
2876:
2874:
1576:{\displaystyle r_{\text{particle}}\,}
449:
444:
3026:
2695:
2680:
1385:is the concentration of solute and
977:{\displaystyle R_{\text{p0.2}}=350}
944:{\displaystyle R_{\text{p0.1}}=310}
627:10% Ni, 1.6% Fe, 1% Mn, balance Cu
24:
3016:, 22nd edition. Industrial Press.
2871:
2777:
2321:{\displaystyle \tau _{\max }=G/30}
1813:Experimental shear strength (GPa)
1493:
1427:
1409:Particle/precipitate strengthening
1237:
1118:
25:
3132:
1810:Theoretical shear strength (GPa)
1096:
2780:Mechanical behavior of materials
2520:Beer, Johnston & Dewolf 2001
2386:Specified minimum yield strength
1483:and the bowing/ringing formula:
482:Steel, high strength alloy ASTM
2980:Advanced Mechanics of Materials
2909:
2818:
2719:
2710:
2701:
2674:
2616:
1318:, related to the yield stress,
1030:Usage in structural engineering
1004:{\displaystyle R_{\text{p0.2}}}
2594:
2583:
2551:
2525:
2513:
2487:
2478:
2452:
2413:
1417:The shearing formula goes as:
888:Elastic limit (yield strength)
434:
282:behavior and the beginning of
13:
1:
3049:Mechanical Engineering Design
2963:(3rd ed.). McGraw-Hill.
2892:www.baileymetalprocessing.com
2778:H., Courtney, Thomas (2005).
2668:10.1016/S0377-0257(98)00094-9
2406:
2217:{\displaystyle \tau _{\max }}
3051:, 5th edition. McGraw Hill.
3033:. City: Albion/Horwood Pub.
2332:Yield point elongation (YPE)
1643:Grain boundary strengthening
1215:Solid solution strengthening
1211:is the dislocation density.
1091:Grain boundary strengthening
1081:Solid solution strengthening
1014:Upper and lower yield points
496:Steel, prestressing strands
278:that indicates the limit of
7:
2374:
1773:is a material constant, and
1744:{\displaystyle \sigma _{0}}
1180:{\displaystyle \sigma _{y}}
1086:Precipitation strengthening
867:The lowest stress at which
438:
199:Metal-induced embrittlement
10:
3137:
2438:10.1007/s40799-023-00626-4
1800:Theoretical yield strength
1038:
189:Liquid metal embrittlement
29:
3066:. New York: McGraw-Hill.
2753:10.1007/s11665-008-9225-5
2391:Ultimate tensile strength
1398:{\displaystyle \epsilon }
534:High-density polyethylene
361:strain hardening exponent
353:ultimate tensile strength
204:Stress corrosion cracking
95:{\displaystyle \epsilon }
78:, shown as a function of
1583:is the particle radius,
1063:Strengthening mechanisms
136:Mechanical failure modes
3116:Deformation (mechanics)
2997:(9th ed.). Wiley.
2559:"unitex-deutschland.eu"
2426:Experimental Techniques
1057:Indentation plastometry
563:AISI 302 – cold-rolled
209:Sulfide stress cracking
71:{\displaystyle \sigma }
32:Material failure theory
2960:Mechanics of Materials
2322:
2278:
2218:
2188:
2108:
1974:
1951:
1789:
1767:
1745:
1712:
1633:
1605:
1577:
1546:
1474:
1399:
1379:
1352:
1332:
1308:
1285:
1205:
1181:
1151:
1005:
978:
945:
417:
336:which is normally not
179:Hydrogen embrittlement
130:
96:
72:
2611:Mechanical Metallurgy
2396:Yield curve (physics)
2323:
2279:
2219:
2189:
2109:
1975:
1952:
1790:
1768:
1746:
1713:
1634:
1606:
1578:
1547:
1475:
1400:
1380:
1378:{\displaystyle C_{s}}
1353:
1333:
1309:
1307:{\displaystyle \tau }
1286:
1206:
1204:{\displaystyle \rho }
1182:
1152:
1017:Some metals, such as
1006:
979:
946:
874:Proportionality limit
418:
113:Proportionality limit
102:):
97:
73:
42:
3106:Plasticity (physics)
3096:Elasticity (physics)
3014:Machinery's Handbook
2381:Plasticity (physics)
2350:Cottrell atmospheres
2291:
2235:
2201:
2124:
1987:
1964:
1896:
1779:
1757:
1728:
1655:
1615:
1587:
1559:
1490:
1424:
1389:
1362:
1342:
1322:
1298:
1234:
1195:
1164:
1115:
1052:Indentation hardness
988:
955:
922:
905:Offset yield point (
858:stress–strain curves
738:Aluminium (annealed)
374:
86:
62:
3121:Structural analysis
3081:Engineer's Handbook
3030:Mechanics of Solids
2839:2009NanoL...9.3048R
2744:2008JMEP...17..888P
2613:, McGraw-Hill, 1986
1555:In these formulas,
296:plastic deformation
276:stress-strain curve
194:Mechanical overload
44:Stress–strain curve
2782:. Waveland Press.
2539:on 14 October 2011
2484:ASTM A228-A228M-14
2318:
2274:
2214:
2197:Giving a value of
2184:
2104:
1970:
1947:
1795:is the grain size.
1785:
1763:
1741:
1708:
1629:
1601:
1573:
1542:
1470:
1395:
1375:
1348:
1328:
1304:
1281:
1201:
1177:
1147:
1001:
974:
941:
916:offset yield point
864:True elastic limit
577:4.5% C, ASTM A-48
471:Steel, API 5L X65
413:
288:deform elastically
274:is the point on a
131:
108:True elastic limit
92:
68:
3073:978-0-07-072542-3
3040:978-1-898563-67-9
3027:Ross, C. (1999).
3004:978-0-471-65653-1
2970:978-0-07-365935-0
2948:978-0-07-142867-5
2927:978-0-07-004997-0
2857:10.1021/nl9015107
2640:978-0-395-18916-0
2272:
2172:
2151:
2092:
2070:
2032:
2014:
1973:{\displaystyle b}
1941:
1872:
1871:
1788:{\displaystyle d}
1766:{\displaystyle k}
1703:
1625:
1597:
1569:
1540:
1536:
1520:
1467:
1458:
1455:
1445:
1351:{\displaystyle b}
1331:{\displaystyle G}
1278:
1264:
1145:
998:
965:
932:
854:
853:
749:Copper (annealed)
450:Ultimate strength
311:material property
264:materials science
260:
259:
154:Corrosion fatigue
52:nonferrous alloys
16:(Redirected from
3128:
3077:
3044:
3008:
2974:
2952:
2931:
2903:
2902:
2900:
2898:
2884:
2869:
2868:
2850:
2833:(8): 3048–3052.
2822:
2816:
2815:
2809:
2801:
2775:
2766:
2765:
2755:
2723:
2717:
2716:Degarmo, p. 377.
2714:
2708:
2705:
2699:
2693:
2684:
2678:
2672:
2671:
2662:(1–2): 133–178.
2651:
2645:
2644:
2620:
2614:
2607:
2601:
2598:
2592:
2587:
2581:
2580:
2578:
2576:
2571:on 25 March 2012
2570:
2564:. Archived from
2563:
2555:
2549:
2548:
2546:
2544:
2535:. Archived from
2529:
2523:
2517:
2511:
2510:
2508:
2506:
2497:. Archived from
2491:
2485:
2482:
2476:
2475:
2473:
2471:
2462:. Archived from
2456:
2450:
2449:
2432:(6): 1311–1322.
2417:
2327:
2325:
2324:
2319:
2314:
2303:
2302:
2283:
2281:
2280:
2275:
2273:
2271:
2260:
2252:
2247:
2246:
2223:
2221:
2220:
2215:
2213:
2212:
2193:
2191:
2190:
2185:
2183:
2182:
2173:
2168:
2157:
2152:
2150:
2142:
2134:
2113:
2111:
2110:
2105:
2103:
2102:
2093:
2088:
2080:
2075:
2071:
2066:
2055:
2043:
2042:
2033:
2028:
2020:
2015:
2013:
2005:
1997:
1979:
1977:
1976:
1971:
1956:
1954:
1953:
1948:
1946:
1942:
1937:
1926:
1914:
1913:
1804:
1803:
1794:
1792:
1791:
1786:
1772:
1770:
1769:
1764:
1750:
1748:
1747:
1742:
1740:
1739:
1717:
1715:
1714:
1709:
1706:
1705:
1704:
1696:
1680:
1679:
1667:
1666:
1638:
1636:
1635:
1630:
1627:
1626:
1623:
1610:
1608:
1607:
1602:
1599:
1598:
1595:
1582:
1580:
1579:
1574:
1571:
1570:
1567:
1551:
1549:
1548:
1543:
1541:
1539:
1538:
1537:
1534:
1522:
1521:
1518:
1511:
1503:
1479:
1477:
1476:
1471:
1469:
1468:
1465:
1459:
1457:
1456:
1453:
1447:
1446:
1443:
1437:
1404:
1402:
1401:
1396:
1384:
1382:
1381:
1376:
1374:
1373:
1357:
1355:
1354:
1349:
1337:
1335:
1334:
1329:
1313:
1311:
1310:
1305:
1290:
1288:
1287:
1282:
1280:
1279:
1271:
1265:
1263:
1262:
1253:
1210:
1208:
1207:
1202:
1186:
1184:
1183:
1178:
1176:
1175:
1156:
1154:
1153:
1148:
1146:
1141:
1130:
1129:
1010:
1008:
1007:
1002:
1000:
999:
996:
983:
981:
980:
975:
967:
966:
963:
950:
948:
947:
942:
934:
933:
930:
910:
909:
885:of the material.
727:Nylon, type 6/6
613:Copper 99.9% Cu
439:
422:
420:
419:
414:
412:
411:
399:
398:
386:
385:
342:ultimate failure
252:
245:
238:
133:
132:
101:
99:
98:
93:
77:
75:
74:
69:
46:showing typical
21:
3136:
3135:
3131:
3130:
3129:
3127:
3126:
3125:
3111:Solid mechanics
3086:
3085:
3074:
3041:
3005:
2971:
2949:
2928:
2912:
2907:
2906:
2896:
2894:
2886:
2885:
2872:
2848:10.1.1.702.1801
2823:
2819:
2803:
2802:
2790:
2776:
2769:
2724:
2720:
2715:
2711:
2707:ISO 6892-1:2009
2706:
2702:
2694:
2687:
2679:
2675:
2652:
2648:
2641:
2621:
2617:
2608:
2604:
2599:
2595:
2588:
2584:
2574:
2572:
2568:
2561:
2557:
2556:
2552:
2542:
2540:
2531:
2530:
2526:
2518:
2514:
2504:
2502:
2501:on 19 July 2011
2493:
2492:
2488:
2483:
2479:
2469:
2467:
2466:on 22 June 2012
2458:
2457:
2453:
2418:
2414:
2409:
2377:
2334:
2310:
2298:
2294:
2292:
2289:
2288:
2261:
2253:
2251:
2242:
2238:
2236:
2233:
2232:
2227:
2208:
2204:
2202:
2199:
2198:
2178:
2174:
2158:
2156:
2143:
2135:
2133:
2125:
2122:
2121:
2098:
2094:
2081:
2079:
2056:
2054:
2050:
2038:
2034:
2021:
2019:
2006:
1998:
1996:
1988:
1985:
1984:
1965:
1962:
1961:
1927:
1925:
1921:
1909:
1905:
1897:
1894:
1893:
1885:
1802:
1780:
1777:
1776:
1758:
1755:
1754:
1735:
1731:
1729:
1726:
1725:
1695:
1691:
1687:
1675:
1671:
1662:
1658:
1656:
1653:
1652:
1645:
1622:
1618:
1616:
1613:
1612:
1596:particle-matrix
1594:
1590:
1588:
1585:
1584:
1566:
1562:
1560:
1557:
1556:
1533:
1529:
1517:
1513:
1512:
1504:
1502:
1491:
1488:
1487:
1466:particle-matrix
1464:
1460:
1452:
1448:
1442:
1438:
1436:
1425:
1422:
1421:
1411:
1390:
1387:
1386:
1369:
1365:
1363:
1360:
1359:
1343:
1340:
1339:
1323:
1320:
1319:
1299:
1296:
1295:
1270:
1266:
1258:
1254:
1252:
1235:
1232:
1231:
1217:
1196:
1193:
1192:
1171:
1167:
1165:
1162:
1161:
1140:
1125:
1121:
1116:
1113:
1112:
1099:
1065:
1041:
1032:
995:
991:
989:
986:
985:
962:
958:
956:
953:
952:
929:
925:
923:
920:
919:
907:
906:
883:elastic modulus
760:Iron (annealed)
600:Aluminium alloy
561:Stainless steel
451:
446:
437:
429:yield criterion
407:
403:
394:
390:
381:
377:
375:
372:
371:
368:solid mechanics
256:
129:
128:
87:
84:
83:
63:
60:
59:
35:
28:
23:
22:
15:
12:
11:
5:
3134:
3124:
3123:
3118:
3113:
3108:
3103:
3098:
3084:
3083:
3078:
3072:
3059:
3045:
3039:
3024:
3010:
3003:
2990:
2976:
2969:
2954:
2947:
2932:
2926:
2911:
2908:
2905:
2904:
2870:
2817:
2789:978-1577664253
2788:
2767:
2738:(6): 888–893.
2718:
2709:
2700:
2685:
2673:
2646:
2639:
2615:
2602:
2593:
2582:
2550:
2524:
2522:, p. 746.
2512:
2495:"complore.com"
2486:
2477:
2451:
2411:
2410:
2408:
2405:
2404:
2403:
2398:
2393:
2388:
2383:
2376:
2373:
2367:, and reduces
2333:
2330:
2317:
2313:
2309:
2306:
2301:
2297:
2285:
2284:
2270:
2267:
2264:
2259:
2256:
2250:
2245:
2241:
2225:
2211:
2207:
2195:
2194:
2181:
2177:
2171:
2167:
2164:
2161:
2155:
2149:
2146:
2141:
2138:
2132:
2129:
2115:
2114:
2101:
2097:
2091:
2087:
2084:
2078:
2074:
2069:
2065:
2062:
2059:
2053:
2049:
2046:
2041:
2037:
2031:
2027:
2024:
2018:
2012:
2009:
2004:
2001:
1995:
1992:
1969:
1958:
1957:
1945:
1940:
1936:
1933:
1930:
1924:
1920:
1917:
1912:
1908:
1904:
1901:
1883:
1870:
1869:
1866:
1863:
1859:
1858:
1855:
1852:
1848:
1847:
1844:
1841:
1837:
1836:
1833:
1830:
1826:
1825:
1822:
1819:
1815:
1814:
1811:
1808:
1801:
1798:
1797:
1796:
1784:
1774:
1762:
1752:
1738:
1734:
1719:
1718:
1702:
1699:
1694:
1690:
1686:
1683:
1678:
1674:
1670:
1665:
1661:
1644:
1641:
1621:
1593:
1565:
1553:
1552:
1532:
1528:
1525:
1516:
1510:
1507:
1501:
1498:
1495:
1481:
1480:
1463:
1451:
1441:
1435:
1432:
1429:
1410:
1407:
1394:
1372:
1368:
1347:
1327:
1303:
1292:
1291:
1277:
1274:
1269:
1261:
1257:
1251:
1248:
1245:
1242:
1239:
1216:
1213:
1200:
1189:Burgers vector
1174:
1170:
1158:
1157:
1144:
1139:
1136:
1133:
1128:
1124:
1120:
1098:
1097:Work hardening
1095:
1094:
1093:
1088:
1083:
1078:
1076:Work hardening
1064:
1061:
1040:
1037:
1031:
1028:
1027:
1026:
1015:
1012:
994:
973:
970:
961:
940:
937:
928:
912:
903:
900:
897:
889:
886:
875:
872:
865:
852:
851:
848:
845:
838:
837:
834:
831:
824:
823:
820:
817:
810:
809:
806:
803:
796:
795:
792:
789:
782:
781:
778:
775:
768:
767:
764:
761:
757:
756:
753:
750:
746:
745:
742:
739:
735:
734:
731:
728:
724:
723:
720:
717:
710:
709:
706:
703:
697:
696:
693:
690:
675:
674:
671:
668:
661:
660:
657:
654:
648:
647:
644:
641:
635:
634:
631:
628:
621:
620:
617:
614:
610:
609:
606:
603:
596:
595:
592:
589:
588:(6% Al, 4% V)
586:Titanium alloy
582:
581:
578:
571:
570:
567:
564:
557:
556:
553:
550:
544:
543:
540:
537:
530:
529:
526:
524:
517:
516:
513:
510:
504:
503:
500:
497:
493:
492:
489:
486:
479:
478:
475:
472:
468:
467:
464:
461:
454:
453:
448:
445:Yield strength
443:
436:
433:
410:
406:
402:
397:
393:
389:
384:
380:
303:yield strength
258:
257:
255:
254:
247:
240:
232:
229:
228:
227:
226:
221:
216:
211:
206:
201:
196:
191:
186:
181:
176:
171:
166:
161:
156:
151:
146:
138:
137:
127:
126:
124:yield strength
120:
115:
110:
104:
103:
91:
67:
26:
18:Yield strength
9:
6:
4:
3:
2:
3133:
3122:
3119:
3117:
3114:
3112:
3109:
3107:
3104:
3102:
3099:
3097:
3094:
3093:
3091:
3082:
3079:
3075:
3069:
3065:
3060:
3058:
3057:0-07-056899-5
3054:
3050:
3046:
3042:
3036:
3032:
3031:
3025:
3023:
3022:0-8311-1155-0
3019:
3015:
3011:
3006:
3000:
2996:
2991:
2989:
2988:0-471-55157-0
2985:
2981:
2977:
2972:
2966:
2962:
2961:
2955:
2950:
2944:
2940:
2939:
2933:
2929:
2923:
2919:
2914:
2913:
2893:
2889:
2883:
2881:
2879:
2877:
2875:
2866:
2862:
2858:
2854:
2849:
2844:
2840:
2836:
2832:
2828:
2821:
2813:
2807:
2799:
2795:
2791:
2785:
2781:
2774:
2772:
2763:
2759:
2754:
2749:
2745:
2741:
2737:
2733:
2729:
2722:
2713:
2704:
2698:, p. 59.
2697:
2692:
2690:
2683:, p. 56.
2682:
2677:
2669:
2665:
2661:
2657:
2650:
2642:
2636:
2632:
2628:
2627:
2619:
2612:
2606:
2597:
2591:
2586:
2567:
2560:
2554:
2538:
2534:
2528:
2521:
2516:
2500:
2496:
2490:
2481:
2465:
2461:
2460:"ussteel.com"
2455:
2447:
2443:
2439:
2435:
2431:
2427:
2423:
2416:
2412:
2402:
2401:Yield surface
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2378:
2372:
2370:
2366:
2361:
2357:
2353:
2351:
2345:
2342:
2339:
2329:
2315:
2311:
2307:
2304:
2295:
2268:
2265:
2262:
2257:
2254:
2248:
2239:
2231:
2230:
2229:
2205:
2175:
2169:
2165:
2162:
2159:
2153:
2147:
2144:
2139:
2136:
2130:
2127:
2120:
2119:
2118:
2095:
2089:
2085:
2082:
2076:
2072:
2067:
2063:
2060:
2057:
2051:
2047:
2044:
2035:
2029:
2025:
2022:
2016:
2010:
2007:
2002:
1999:
1993:
1990:
1983:
1982:
1981:
1967:
1943:
1938:
1934:
1931:
1928:
1922:
1918:
1915:
1906:
1902:
1899:
1892:
1891:
1890:
1887:
1879:
1875:
1867:
1864:
1861:
1860:
1856:
1853:
1850:
1849:
1845:
1842:
1839:
1838:
1834:
1831:
1828:
1827:
1823:
1820:
1817:
1816:
1812:
1809:
1806:
1805:
1782:
1775:
1760:
1753:
1736:
1732:
1724:
1723:
1722:
1700:
1697:
1692:
1688:
1684:
1681:
1676:
1672:
1668:
1663:
1659:
1651:
1650:
1649:
1640:
1624:interparticle
1619:
1591:
1563:
1530:
1526:
1523:
1519:interparticle
1514:
1508:
1505:
1499:
1496:
1486:
1485:
1484:
1461:
1454:interparticle
1449:
1439:
1433:
1430:
1420:
1419:
1418:
1415:
1406:
1392:
1370:
1366:
1345:
1325:
1317:
1301:
1275:
1272:
1267:
1259:
1255:
1249:
1246:
1243:
1240:
1230:
1229:
1228:
1225:
1222:
1212:
1198:
1190:
1172:
1168:
1142:
1137:
1134:
1131:
1126:
1122:
1111:
1110:
1109:
1106:
1104:
1092:
1089:
1087:
1084:
1082:
1079:
1077:
1074:
1073:
1072:
1069:
1060:
1058:
1053:
1049:
1047:
1046:tensile test.
1036:
1024:
1020:
1016:
1013:
992:
971:
968:
959:
938:
935:
926:
917:
913:
904:
901:
898:
895:
890:
887:
884:
880:
876:
873:
870:
866:
863:
862:
861:
859:
849:
846:
843:
840:
839:
835:
832:
829:
826:
825:
821:
818:
815:
812:
811:
807:
804:
801:
798:
797:
793:
790:
787:
784:
783:
779:
776:
773:
770:
769:
765:
762:
759:
758:
754:
751:
748:
747:
743:
740:
737:
736:
732:
729:
726:
725:
721:
718:
715:
712:
711:
707:
704:
702:
699:
698:
694:
691:
688:
684:
680:
677:
676:
672:
669:
666:
663:
662:
658:
655:
653:
650:
649:
645:
642:
640:
637:
636:
632:
629:
626:
623:
622:
618:
615:
612:
611:
607:
604:
601:
598:
597:
593:
590:
587:
584:
583:
579:
576:
573:
572:
568:
565:
562:
559:
558:
554:
551:
549:
548:Polypropylene
546:
545:
541:
538:
535:
532:
531:
527:
525:
522:
519:
518:
514:
511:
509:
506:
505:
501:
498:
495:
494:
490:
487:
485:
481:
480:
476:
473:
470:
469:
465:
462:
460:
456:
455:
441:
440:
432:
430:
426:
425:yield surface
408:
404:
400:
395:
391:
387:
382:
378:
369:
364:
362:
358:
354:
350:
345:
343:
339:
335:
331:
327:
324:
320:
316:
312:
308:
304:
299:
297:
293:
289:
285:
281:
277:
273:
269:
265:
253:
248:
246:
241:
239:
234:
233:
231:
230:
225:
222:
220:
217:
215:
214:Thermal shock
212:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
185:
182:
180:
177:
175:
172:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
141:
140:
139:
135:
134:
125:
121:
119:
118:Elastic limit
116:
114:
111:
109:
106:
105:
89:
81:
65:
57:
53:
50:behavior for
49:
45:
41:
37:
33:
19:
3063:
3048:
3029:
3013:
2994:
2979:
2959:
2937:
2917:
2910:Bibliography
2895:. Retrieved
2891:
2830:
2827:Nano Letters
2826:
2820:
2779:
2735:
2731:
2721:
2712:
2703:
2676:
2659:
2655:
2649:
2625:
2618:
2610:
2605:
2596:
2585:
2573:. Retrieved
2566:the original
2553:
2541:. Retrieved
2537:the original
2527:
2515:
2505:10 September
2503:. Retrieved
2499:the original
2489:
2480:
2468:. Retrieved
2464:the original
2454:
2429:
2425:
2415:
2365:roll forming
2362:
2358:
2354:
2346:
2335:
2286:
2196:
2116:
1959:
1888:
1880:
1876:
1873:
1720:
1646:
1554:
1482:
1416:
1412:
1316:shear stress
1293:
1226:
1218:
1159:
1107:
1103:dislocations
1100:
1070:
1066:
1050:
1042:
1033:
1025:can develop.
1023:Lüders bands
915:
908:proof stress
869:dislocations
855:
521:Carbon fiber
428:
365:
346:
338:catastrophic
334:failure mode
330:proof stress
329:
307:yield stress
306:
302:
300:
271:
261:
223:
47:
36:
2609:G. Dieter,
899:Yield point
879:Hooke's law
652:Spider silk
625:Cupronickel
435:Definitions
323:cold-worked
272:yield point
268:engineering
3090:Categories
2590:matweb.com
2407:References
2369:springback
2228:equal to:
1862:α-Fe
1019:mild steel
894:elastomers
844:(annealed)
830:(annealed)
816:(annealed)
802:(annealed)
788:(annealed)
774:(annealed)
523:(CF, CFK)
515:1740–3300
508:Piano wire
3101:Mechanics
2843:CiteSeerX
2806:cite book
2798:894800884
2762:135890256
2696:Ross 1999
2681:Ross 1999
2543:18 August
2446:1747-1567
2296:τ
2266:π
2240:τ
2206:τ
2176:τ
2163:π
2148:γ
2140:τ
2096:τ
2086:π
2061:π
2048:
2036:τ
2026:π
2003:τ
1932:π
1919:
1907:τ
1900:τ
1807:Material
1733:σ
1693:−
1673:σ
1660:σ
1592:γ
1524:−
1497:τ
1494:Δ
1462:γ
1431:τ
1428:Δ
1393:ϵ
1302:τ
1268:ϵ
1241:τ
1238:Δ
1199:ρ
1169:σ
1143:ρ
1123:σ
1119:Δ
791:5000–9000
656:1150 (??)
575:Cast iron
459:A36 steel
442:Material
423:) with a
405:σ
392:σ
379:σ
357:pipelines
340:, unlike
319:aluminium
149:Corrosion
90:ϵ
66:σ
2865:19637912
2375:See also
2338:annealed
1568:particle
1535:particle
1444:particle
1221:alloying
850:550–620
842:Tungsten
836:240–370
828:Titanium
800:Tantalum
780:140–195
665:Silkworm
602:2014-T6
555:19.7–80
224:Yielding
174:Fracture
144:Buckling
2897:16 June
2835:Bibcode
2740:Bibcode
2575:15 June
2470:15 June
1314:is the
1039:Testing
951:MPa or
833:100–225
822:15–200
794:
786:Silicon
719:104–121
716:(limb)
673:
536:(HDPE)
349:ductile
284:plastic
280:elastic
169:Fouling
164:Fatigue
122:Offset
82:,
58:,
3070:
3055:
3037:
3020:
3001:
2986:
2967:
2945:
2924:
2863:
2845:
2796:
2786:
2760:
2637:
2444:
2224:τ
1960:where
1721:where
1294:where
1191:, and
1160:where
772:Nickel
763:80–100
744:40–50
701:UHMWPE
687:Twaron
683:Kevlar
679:Aramid
643:200+ ~
512:
452:(MPa)
447:(MPa)
292:stress
270:, the
184:Impact
80:strain
56:stress
2758:S2CID
2569:(PDF)
2562:(PDF)
2341:steel
1868:2.75
1846:0.49
1835:0.78
1824:0.37
777:14–35
741:15–20
695:3757
667:silk
659:1400
639:Brass
552:12–43
539:26–33
528:5650
502:1860
457:ASTM
427:or a
326:steel
309:is a
159:Creep
48:yield
3068:ISBN
3053:ISBN
3035:ISBN
3018:ISBN
2999:ISBN
2984:ISBN
2965:ISBN
2943:ISBN
2922:ISBN
2899:2024
2861:PMID
2812:link
2794:OCLC
2784:ISBN
2635:ISBN
2577:2011
2545:2010
2507:2010
2472:2011
2442:ISSN
1865:2.6
1857:3.2
1854:2.6
1843:1.4
1832:0.9
1821:1.0
1338:and
997:p0.2
964:p0.2
931:p0.1
819:9–14
808:200
766:350
755:210
722:130
714:Bone
692:3620
646:550
633:350
619:220
608:455
594:900
580:172
569:860
499:1650
491:760
484:A514
477:531
466:400
347:For
321:and
315:load
301:The
266:and
219:Wear
2853:doi
2748:doi
2664:doi
2434:doi
2300:max
2244:max
2226:max
2210:max
2180:max
2100:max
2045:cos
2040:max
1916:sin
1911:max
1884:max
1851:Ni
1840:Cu
1829:Al
1818:Ag
1219:By
972:350
939:310
847:550
814:Tin
805:180
733:75
708:35
685:or
670:500
630:130
605:400
591:830
566:520
542:37
488:690
474:448
463:250
366:In
344:.
305:or
262:In
3092::
2890:.
2873:^
2859:.
2851:.
2841:.
2829:.
2808:}}
2804:{{
2792:.
2770:^
2756:.
2746:.
2736:17
2734:.
2730:.
2688:^
2660:81
2658:.
2633:.
2631:61
2440:.
2430:47
2428:.
2424:.
2352:.
2328:.
2316:30
1886:.
1059:.
752:33
730:45
705:20
689:)
616:70
363:.
298:.
3076:.
3043:.
3009:.
3007:.
2975:.
2973:.
2953:.
2951:.
2930:.
2901:.
2867:.
2855::
2837::
2831:9
2814:)
2800:.
2764:.
2750::
2742::
2670:.
2666::
2643:.
2579:.
2547:.
2509:.
2474:.
2448:.
2436::
2312:/
2308:G
2305:=
2269:a
2263:2
2258:b
2255:G
2249:=
2170:b
2166:a
2160:2
2154:=
2145:d
2137:d
2131:=
2128:G
2090:b
2083:2
2077:=
2073:)
2068:b
2064:x
2058:2
2052:(
2030:b
2023:2
2017:=
2011:x
2008:d
2000:d
1994:=
1991:G
1968:b
1944:)
1939:b
1935:x
1929:2
1923:(
1903:=
1783:d
1761:k
1737:0
1701:2
1698:1
1689:d
1685:k
1682:+
1677:0
1669:=
1664:y
1620:l
1564:r
1531:r
1527:2
1515:l
1509:b
1506:G
1500:=
1450:l
1440:r
1434:=
1371:s
1367:C
1346:b
1326:G
1276:2
1273:3
1260:s
1256:C
1250:b
1247:G
1244:=
1173:y
1138:b
1135:G
1132:=
1127:y
993:R
969:=
960:R
936:=
927:R
911:)
681:(
409:3
401:,
396:2
388:,
383:1
251:e
244:t
237:v
54:(
34:.
20:)
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