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A standard uniaxial tensile test, which establishes the engineering stress-strain relationship, in general, provides the basic mechanical properties of steel required by a structural designer. Modern numerical analysis techniques used for analysis of large strain problems such as failure analysis of steel structures and elements metal forming, metal cutting, and so forth, will require implementation and use of true stress-true strain material characterization. This paper establishes a five stage true stress-strain model for A992 and 350W steel grades, which can capture the behavior of structural steel, including the postultimate behavior of steel, until fracture. The proposed model uses a power law in strain hardening range and a weighted power law in the postultimate range. The true stress-true strain model parameters were established through matching of numerical analysis results with the corresponding standard uniaxial tensile test experimental results. The material constitutive relationship so derived was then applied to predict the load-deformation behavior of coupons with a hole in the middle region subjected to direct tension loading. The predicted load-deformation behavior of perforated tension coupons agreed well with the corresponding test results validating the proposed characterization of the true stress-true strain relationship for structural steel.

The finite-element- (FE-) method-based numerical analysis and other numerical analysis techniques are widely used in research involving structural steel and in the analysis and design of steel structures and elements. In research, numerical modeling techniques are often used to effectively expand the limited experimental results and used to investigate the influence of relevant parameters associated with a problem. Such simulations models for structural steel, however, require the use of realistic material stress-strain relationships, often extending up to fracture. Mechanical behavior of metallic type material, such as that of steel, is generally established by means of uniaxial tension test. Such tension test protocol [

The engineering stress-strain relations and the proposed true stress-true strain material model.

A standard uniaxial tensile test, in general, provides the basic mechanical properties of steel required by a structural designer; thus, the mill certificates provide properties such as yield strength

During the initial stages of loading, stress varies linearly proportional to strain (up to a proportional limit). The proportional limit stress

This range represents a region between the proportional limit and the yield point. The yield point

Some steels may exhibit yield plateau. The engineering stress in this region can be assumed as a constant value of

At the end of yield plateau, strain hardening begins with a subsequent increase in stress. Region-IV includes the strain hardening range up to ultimate strength when the test specimen may begin to exhibit necking. Though this region involves a nonlinear stress-strain relation, it is postulated that the true stress and the true strain can be obtained using the relations

This region represents the behavior of the material in the apparent strain softening region. As explained earlier, the apparent strain softening is due to the use of the original cross-sectional area, and should the actual cross-sectional area be used, the stress and strain would continue to increase. The true stress-strain relations cannot be established in this region from engineering stress-strain values; thus, an experimental-numerical iterative approach was used in this study to derive the true stress-strain material characterization for this region. Zhano and Li [

In summary, this paper proposes a five stage characterization for the true stress-true strain relations for structural steel. The following parameters, namely, initial modulus of elasticity

The true stress-true strain model parameters were established through amalgamation of experimental and numerical modeling techniques. The test program considered twenty eight tensile coupons, fourteen each from two different steel grades, namely, ASTM A992 steel and the 350W steel. The tensile coupons for this investigation were cut along the rolling direction (length direction) of standard W310 × 39 (W12 × 26) wide flange beam sections. For each steel grade, eight coupons were taken from the flanges and six coupons were from the web of the section. The fabrication dimensions of the tensile coupons were in accordance with ASTM A370-10 [

Summary of mechanical properties of solid coupons (no hole).

Steel | Specimen ID | |||||||||||

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) |

A992 | A992-F1-1.0 | 204 | 422 | 0.0022 | 11.5 | 445 | 0.0042 | 0.0042 | 1.0 | 579 | 0.1348 | 0.2041 |

A992-F2-1.0 | 203 | 418 | 0.0022 | 12.4 | 443 | 0.0042 | 0.0042 | 1.0 | 585 | 0.1353 | 0.2106 | |

A992-F3-1.0 | 201 | 390 | 0.0020 | 25.7 | 445 | 0.0042 | 0.0042 | 1.0 | 568 | 0.1441 | 0.2100 | |

A992-W1-1.0 | 202 | 405 | 0.0020 | 00.0 | 405 | 0.0020 | 0.0156 | 7.8 | 568 | 0.1620 | 0.2083 | |

A992-W2-1.0 | 201 | 415 | 0.0021 | 00.0 | 415 | 0.0021 | 0.0132 | 6.3 | 591 | 0.1599 | 0.2023 | |

A992-W3-1.0 | 202 | 406 | 0.0020 | 00.0 | 406 | 0.0020 | 0.0154 | 7.7 | 561 | 0.1446 | 0.2308 | |

350W | 350W-F1-1.0 | 208 | 392 | 0.0020 | 17.2 | 427 | 0.0040 | 0.0040 | 1.0 | 581 | 0.1412 | 0.2282 |

350W-F2-1.0 | 215 | 403 | 0.0021 | 11.1 | 424 | 0.0040 | 0.0040 | 1.0 | 575 | 0.1443 | 0.2083 | |

350W-F3-1.0 | 216 | 400 | 0.0020 | 15.6 | 430 | 0.0040 | 0.0040 | 1.0 | 578 | 0.1307 | 0.2240 | |

350W-W1-1.0 | 195 | 414 | 0.0021 | 00.0 | 414 | 0.0021 | 0.0160 | 7.6 | 571 | 0.1595 | 0.2054 | |

350W-W2-1.0 | 195 | 413 | 0.0021 | 00.0 | 413 | 0.0021 | 0.0140 | 6.7 | 593 | 0.1292 | 0.1771 | |

350W-W3-1.0 | 213 | 422 | 0.0020 | 00.0 | 422 | 0.0020 | 0.0158 | 7.9 | 581 | 0.1702 | 0.2025 | |

The tension coupons (a) with no holes and (b) with a central hole.

The coupons were tension tested in a Tinius Olsen machine with an axial load capacity of 600 kN. Each test specimen was first aligned vertically and centered with respect to the grips of the machine’s loading platforms. Two extensometers having gauge lengths of 200 mm and 50 mm were attached on either face of the test coupon. The larger extensometer was used to establish the overall engineering stress-strain curve of the coupons, whereas the smaller extensometer, which had a greater sensitivity, allowed a more accurate estimation of the initial modulus

True stress-true strain model parameters for A992 and 350W steel grades.

Region-I | Region-II | Region-III | Region-IV | Region-V | |
---|---|---|---|---|---|

Steel grade-element | Linear elastic range | Nonlinear elastic range | Yield plateau range | Strain hardening range | Postultimate strength range |

A992-flange | |||||

A992-web | |||||

350W-flange | |||||

350W-web |

Experimental engineering stress-engineering strain relationships (over 200 mm gauge length).

The Region-IV requires the power law parameter

True stress-true strain relationships in region IV—350W-web.

The Region-V requires establishment of a weighting constant

Figure

Comparison of stresses and strains at fracture.

Steel | Specimen ID | Experimental | FEM |
(Exp/FEM)_{stress at fracture} |
(Exp/FEM)_{strain at fracture} | ||||

Stress at fracture (MPa) | Strain at fracture (mm/mm) | Stress at | Strain at | ||||||

A992 | A992-F1-1.0 | 480 | 477* | 0.2162 | 0.2117* | 486 | 0.2098 | 0.98 | 1.00 |

A992-F2-1.0 | 477 | 0.2090 | |||||||

A992-F3-1.0 | 474 | 0.2100 | |||||||

A992-W1-1.0 | 479 | 496* | 0.2083 | 0.2130* | 497 | 0.2168 | 1.00 | 0.98 | |

A992-W2-1.0 | 526 | 0.2023 | |||||||

A992-W3-1.0 | 483 | 0.2285 | |||||||

350W | 350W-F1-1.0 | 487 | 488* | 0.2195 | 0.2169* | 489 | 0.2169 | 1.00 | 1.00 |

350W-F2-1.0 | 487 | 0.2072 | |||||||

350W-F3-1.0 | 490 | 0.2240 | |||||||

350W-W1-1.0 | 499 | 527* | 0.2054 | 0.1955* | 511 | 0.2064 | 1.03 | 0.95 | |

350W-W2-1.0 | 550 | 0.1771 | |||||||

350W-W3-1.0 | 531 | 0.2041 |

*Average values.

Comparison of failure pattern of test sample with FE simulation results.

Influence of weighting constant.

Proposed true stress-true strain model for A992-flange steel.

The proposed true stress-true strain constitutive relations were further validated by incorporating them in a finite element model for tension coupons having a central hole and through comparison of the FE numerical results with the corresponding experimental results. This part of the investigation considered sixteen test cases consisting of eight A992 steel grade and eight 350W steel grade. Each steel grade considered five flange specimens and three web specimens containing a central hole. Holes with net area/gross area ratios varying from 0.5 to 0.9 in increments of 0.1 were prepared for the flange coupons, whereas holes with net area/gross area ratios varying from 0.5 to 0.9 in increments of 0.2 were considered for the web coupons. Figure

Comparison of experimental test results with FE prediction for perforated samples.

Steel grade | Specimen ID | Experimental ultimate stress | FEM ultimate stress | |

(1) | (2) | (3) | (4) | (5) |

A992 | A992-F-0.9 | 547 | 542 | 1.01 |

A992-F-0.8 | 482 | 480 | 1.00 | |

A992-F-0.7 | 429 | 423 | 1.01 | |

A992-F-0.6 | 369 | 362 | 1.02 | |

A992-F-0.5 | 308 | 298 | 1.03 | |

A992-W-0.9 | 528 | 523 | 1.01 | |

A992-W-0.7 | 422 | 418 | 1.01 | |

A992-W-0.5 | 297 | 299 | 0.99 | |

350W | 350W-F-0.9 | 548 | 547 | 1.00 |

350W-F-0.8 | 489 | 488 | 1.00 | |

350W-F-0.7 | 427 | 427 | 1.00 | |

350W-F-0.6 | 366 | 366 | 1.00 | |

350W-F-0.5 | 311 | 312 | 1.00 | |

350W-W-0.9 | 540 | 543 | 0.99 | |

350W-W-0.7 | 417 | 417 | 1.00 | |

350W-W-0.5 | 291 | 302 | 0.96 |

Comparison of failure pattern observed in the experiment and FE simulation-perforated sample.

Analyses of perforated tension coupons—A992 steel grade.

Steel structures construction often necessitates fabrication of holes in the flanges of steel beams [

Elastic modulus, tangent modulus

Engineering stress, engineering stress at proportional limit, engineering stress at yielding, engineering stress at ultimate strength of solid sample

True stress, true stress corresponding to ultimate strength

Ratio between strain at strain hardening and strain at yielding

Power-law material constant

Weight constant

Engineering strain, engineering yield strain, engineering strain at proportional limit, engineering strain at onset of strain hardening, ultimate engineering strain, engineering fracture strain

True strain, true stain corresponding to ultimate strength, true fracture strain.