Failure Strain and Related Triaxiality of Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 Metals, Part I: Experimental Investigation

Abstract

The objective of this study is to develop failure-limit material models for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals, based on parameters of plastic equivalent strain (failure strain) and stress triaxiality. The research is conducted in two parts. This paper presents Part One of the study. In Part One, custom-designed test specimens undergo controlled uniaxial tension and compression testing at ambient temperature. These tests are performed at quasi-static speeds using Universal Testing Machines (UTMs) in accordance with ASTM E8 and ASTM E9 standards. Experimental data, specifically engineering stress–strain and force–displacement curves, are recorded from the onset of loading until specimen fracture, or in the case of compression tests, until the capacity of the testing machine is reached. In Part Two, the emphasis shifts to the calibration of Finite Element Analysis (FEA) models of the custom-designed test specimens. Plastic equivalent strain and the corresponding stress triaxiality values at failure are extracted from each test specimen for the given metal. These values are then systematically plotted onto a single graph to construct the failure-limit curve, which delineates the boundary conditions for material failure. This approach will facilitate the development of a comprehensive material property definition that correlates plastic equivalent strain with stress triaxiality at failure for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals.

1. Introduction

Movement, transport, and storage of hazardous materials are common in the United States and require thorough design safety measures before initiation. Structures containing such materials encounter a range of complex stress conditions when subjected to these types of activities. While design safety is often perceived as the total elimination of risks, it is more accurately characterized by the reduction and management of potential hazards. Risks such as accidental drops due to negligent handling, crushing from improper cargo stacking, and environmental factors such as extreme temperatures, represent just a few examples that, if not appropriately assessed, could result in inaccuracies and premature structural failures.

In the nuclear industry, addressing these risks is particularly critical due to the hazardous nature of the materials involved. Metals such as Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 are commonly used due to their favorable properties, which include high strength, corrosion resistance, and radiation tolerance. These metals are employed in the development of reactor fuels, reactor pressure vessels, piping, and reactor vessel internals. Furthermore, these materials are used in the manufacturing of shipping containers, handling tools, and other components essential for safe and efficient nuclear reactor operation. Ensuring the integrity of these materials through proper design and risk management is vital to prevent structural failures and maintain safety.

Numerous studies have evaluated the structural integrity of transport containers, components, and structures. For instance, Blanton [1] analyzed containers subjected to accidental drops with various impact orientations, determining which scenarios resulted in the greatest damage. Snow et al. [2] initially examined the United States Department of Energy spent fuel container for qualification when subjected to postulated drop events using 304L and 316L metals, then later (Snow et al. [3,4,5,6,7,8]) introduced a strain-based acceptance criterion for inclusion in Section 3 of the ASME Pressure and Boiler Vessel Code.

Additional significant studies contributing to the safe handling and transport of structures, systems, and components (SSCs) include those by Wu et al. [9], Jaksic and Nilsson [10], Aquaro et al. [11], Kim et al. [12], Lin et al. [13], and Oka et al. [14], among others.

These studies examined structures under dynamic loading using conventional engineering methods. While these methods are robust, there remains the potential for premature failure of key components, posing risks of undesirable outcomes and consequences. This concern has been validated by researchers such as Bao and Wierzbicki [15,16,17], who made significant contributions to understanding failure mechanisms. In their studies, Bao and Wierzbicki integrated models such as Gurson’s [18], which describes the nucleation, growth, and coalescence of voids in ductile materials leading to fracture. They also integrated Johnson-Cook [19], which accounts for the effects of strain, strain rate, and temperature on material behavior and is commonly used in high-strain-rate applications such as impact and crash simulations. Additionally, they referenced the Rice–Tracey Model [20], which is focused on the growth of a single void and predicts ductile fracture in metals under triaxial stress. Bao and Wierzbicki concluded that failure mechanisms are diverse and dependent on the type of material system. For instance, the splitting of micro-cracks in brittle heterogeneous materials like concrete, crazing in polymers, and the void nucleation followed by subsequent growth and coalescence in ductile materials are highly sensitive to the state of stress near the fracture zone. Bao and Wierzbicki’s work on stress triaxiality and plastic failure strain has been pivotal in preventing premature material failure. Their research focused on developing criteria to predict the conditions under which materials fail under tension, compression, and complex loadings. They built on the foundational efforts of McClintock [21,22,23], Hancock et al. [24], Thomson and Hancock [25], and Alves and Jones [26]. An aspect of Bao and Wierzbicki’s work proposed establishing a limiting curve based on stress triaxiality and plastic failure strain, below which damage and fracture do not occur. Their research introduced several custom-designed specimens targeting three regions of triaxiality, referred to as negative, low-, and high-stress triaxialities.

Stress triaxiality is defined as the ratio of hydrostatic stress to the equivalent von Mises stress in a material. This value measures the stress state in a material under different loading conditions. Negative triaxiality is associated with compressive hydrostatic stress, where material failure is characterized by shear localization and ductile fracture. Increases in material ductility are observed in this region. Low-stress triaxiality is linked to shear-dominated loading conditions, where shear stress dominates over normal stress. Torsional and other shear-dominating stress states fall within this region. High-stress triaxiality corresponds to tensile hydrostatic stress, often associated with reduced ductility, which is typical in catastrophic failures. These high-stress triaxiality conditions are critical in the design of pressure vessels where catastrophic failures can result in large explosions due to the rapid release of stored energy (pressurized gas or liquid), posing severe risks to safety. Other researchers have also explored material failure linking stress triaxiality and plastic failure strain parameters, including Mirone [27], Yu and Jeong [28], Choung et al. [29], Rodríguez-Millán et al. [30], Kanazawa et al. [31], Brunig et al. [32], Borvik et al. [33], Anderson et al. [34], Huang et al. [35], Li et al. [36], Seidt et al. [37], and Zhang et al. [38].

While there have been studies on carbon steels (Kiran, R., & Khandelwal, K. [39]; Cho et al. [40]) and 304 steels (Othmen et al. [41]; Seo et al. [42]; Xing et al. [43]), there has been a gap in the literature regarding N60 steels. Most studies linking failure strain ($\bar{\epsilon }$) to triaxiality (η) focused more on aluminum alloys. Additionally, no studies have been found that establish failure-limit curves for each of the metals and stress triaxiality regimes targeted in this study, including Aluminum 6061-T6. Consequently, existing data on the material properties of metals such as A36, 304 Stainless Steel, and Nitronic 60 remain limited. While standard mechanical properties for these materials are widely available through organizations like the American Society for Testing and Materials (ASTM), the American Society of Mechanical Engineers (ASME), and the International Organization for Standardization (ISO), failure-limit curves that account for stress triaxiality and equivalent plastic strain are neither common nor universally standardized. This study is motivated by the absence of failure-limit curves for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals. The goal of this study is to systematically establish failure-limit curves for the aforementioned metals at ambient temperatures. A combination of experimental, numerical, and analytical methods will be employed as these metals are subjected to failure loads across a range of stress triaxiality regimes. The stress triaxiality regimes will be defined/controlled using test specimens akin to those described by Bao and Wierzbicki [15,16,17], which include compression, shear, combined shear tension, and tension stress states. A graphical abstract of the study is displayed in Figure 1.

In Part One, the focus is on material selection, specimen design, and laboratory testing. Specifically, this involves selecting appropriate materials, fabricating test specimens, and conducting controlled laboratory tests to obtain relevant data.

In Part Two, the emphasis shifts to the calibration of Finite Element Analysis (FEA) models of the specimens using ABAQUS software [44]. Plastic failure strain and the corresponding stress triaxiality values are extracted from each test specimen for the given metal. These values are then systematically plotted onto a single graph to construct the failure-limit curve, which delineates the boundary conditions for material failure. This approach will facilitate the development of a comprehensive material property definition that correlates failure strain (plastic equivalent strain) with stress triaxiality for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals. The failure criterion in the context of metal deformation is often described as the strain at which the material undergoes fracture or catastrophic failure. In the context of this study, “failure” refers to the point where the final load curve slope change occurs that leads to fracture. If an entire cross section suddenly fractured, failure and fracture could occur at the same point. This did not occur in the tests. Rather, a progressive loss of load-carrying capacity led to fracture. In an FEA model, failure can be described as the point where the first element reaches its ultimate plastic equivalent strain (for its triaxiality value) and can no longer carry shear strains (i.e., it reaches failure strain for its triaxiality). After the first element fails, neighboring elements must carry its load, and a progressive loss of load-carrying capacity leads to fracture (similar to the actual test). The failure point is important because it allows for the definition of the limiting plastic equivalent strain at a given triaxiality.

Figure 2 is a typical force–displacement curve obtained from a smooth round bar test specimen of Aluminum 6061-T6, illustrating the distinction between failure and fracture as used in this study. Utilizing the material’s failure point in lieu of the fracture point is conservative, as it will facilitate a curve with a safety margin against fracture.

2. Experiment Design, Methods, and Materials

Achieving the desired stress states listed in the introduction necessitates the use of Universal Test Machines (UTMs), see Figure 3. For this study, tests are conducted under conditions that simulate quasi-static speeds and normal ambient environments. An Instron 5982 UTM with a 22,500 lbf (100 kN) load capacity was used to conduct the tension testing. It was equipped with a data acquisition unit and an AVE-2 non-contact video extensometer, which utilizes digital image correlation (DIC) techniques for in-plane strain measurement. Specifications for the AVE-2 unit are provided in

Table 1. AVE-2 video extensometer specifications.

Parameter	Specification
Lens focal length	0.63 in
Field of view (axial, transverse)	12.2 in, 1.57 in
Minimum gauge length, width	0.23 in, 0.23 in
Resolution	~2.0 × 10−5 in (0.5 μm)
Accuracy	+/− 0.5% of reading

.

A Nikon D700 camera, with a measurement accuracy (measurement accuracy is based on the camera’s relative position to the test specimen) of ~383 pixels/in (9728 pixels/mm), was utilized to capture out-of-plane movements and shape distortions every five seconds during tests. Tests were conducted at a speed of ~0.0013 in/s (2 mm/min), adjustable to ~0.0079 in/s (12 mm/min) for elongations over 5%, per ASTM E8 (control method C). Quality control was ensured using Bluehill Universal software (version 3.72.4715), with results exported in CSV (comma-separated values) format.

Due to significant load variations between compression and tension tests, a different system was used for the uniaxial compression of the cylindrical specimens. These tests were conducted using an Instron 1325 Universal Testing Machine, a hydraulically driven system with a load capacity of up to 225,000 lbf (1000 kN). Unlike the Instron 5982 UTM used for tensile tests, this unit lacked an AVE unit and data collection capability. The Instron 1325 UTM force–displacement data were manually recorded, with displacement measurements taken from the crosshead position. A Canon EOS 90D camera, with a measurement accuracy (measurement accuracy is based on the camera’s relative position to the test specimen) of ~1122 pixels/in (28,500 pixels/mm), was utilized to capture out-of-plane movements and shape distortions every five to ten seconds during tests. Tests were conducted at a speed of 0.02 in/min (0.508 mm/min) per ASTM E9 for metals at room temperature. The uniaxial tension test [45] and the uniaxial compression test [46] are among the most common methods for determining a material’s stress–strain response. The use of these specific standards allows researchers and engineers to compare material properties reliably and ensure accuracy and consistency on an international scale.

The test specimens used in this research were derived from the studies conducted by Bao and Wierzbicki [15,16,17], Driemeier [47], Li [36], Zhu [48], Fu [49], Roy [50], Yan [51], Ganjiani [52], Nam and Choung [53], and Baruscotti [54]. These researchers selected specific specimen geometries to measure the impact of stress triaxiality on fracture initiation. Their research contributed to the development of ductile fracture initiation models that consider both plastic equivalent strain and stress triaxiality. The specimens were specifically engineered to address a range of complex stress conditions resulting from the types of handling activities mentioned earlier in this paper. These stress conditions include, but are not limited to, compression, shear, combined shear/tension, and tension stress states. The geometric dimensions of these test specimens are illustrated in Figure 4.

Table 2. Test specimens.

Test	Drawing No.	Specimen Description	Stress State	Other Studies Using Similar Specimens
1	821449	Smooth round bar	Tension	Bao [15,16,17], Zhu [48], Ganjiani [52]
2	821450	Large-notched round bar	Tension	Bao [15,16,17]
3	821451	Small-notched round bar	Tension	Bao [15,16,17], Zhu [48]
4	821452	Flat grooved plate	Tension	Bao [15,16,17], Zhu [48]
5	821453	Cylinder	Compression	Bao [15,16,17], Li [36], Ganjiani [52]
6	821455	Simple shear plate	Shear	Bao [15,16,17], Zhu [48], Fu [49], Baruscotti [54], Ganjiani [52]
7	821456	Combined shear/tension plate	Shear/Tension	Bao [15,16,17], Driemeier [47], Fu [49], Baruscotti [54], Ganjiani [52]
8	821457	Perforated plate	Tension	Bao [15,16,17], Driemeier [47]
9	821458	Dog bone	Tension	Bao [15,16,17], Roy ’23, Yan [51], Fu [49], Baruscotti [54], Nam [53], Ganjiani [52]
10	821459	Pipe	Tension	Bao [15,16,17]
11	821460	Solid square bar	Tension	Bao [15,16,17]

provides a description of the test specimens, including the stress states expected of each, corresponding drawing designations, and a sample of studies that have used similar test specimens. Drawing numbers were assigned to each specimen for the purposes of fabrication and procurement. The drawing numbers were also used to differentiate the specimen datasets. A total of eleven distinct tests were conducted for each of the four metals: Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60.

Three samples were produced for each test specimen. Each sample was assigned and marked with an identification number (e.g., A-1 for the Aluminum 6061-T6 specimen, sample 1). Prior to testing, the specimens were lightly sprayed with black and white paint to create black-and-white speckle patterns. Using white paint markers, two reference points located at a distance $L_o$ apart (where $L_o$ is the initial gauge length of the specimen) were established to define the gauge length. These patterns and reference points are used to measure surface deformation and strain (see Figure 5).

3. Experimental Data

Engineering stress (σ) versus engineering strain (ε) is automatically generated as output during the tensile test experiment via the Bluehill software version 3.72.4715 provided by the instrument manufacturer. Force–displacement data is obtained by the equations for force (F = σ$\stackrel{·}{A}$ ), where $\stackrel{·}{A}$ is the initial cross-sectional area, and for displacement (δ = ε$L_o$).

Please note that while the stress–strain and force–displacement data are important for FEA calibration and comparison and that the fracture surface (or deformed state as it relates to the cylinder specimens) can be used to infer their failure mechanisms, the failure point on the load curve is of primary interest. Consequently, stress–strain, force–displacement, and fracture surface data are provided for informational purposes.

Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39, Figure 40, Figure 41, Figure 42, Figure 43, Figure 44, Figure 45, Figure 46, Figure 47, Figure 48, Figure 49, Figure 50, Figure 51, Figure 52, Figure 53, Figure 54, Figure 55, Figure 56, Figure 57, Figure 58, Figure 59 and Figure 60 illustrate the fractured specimens of the uniaxial tensile and compression tested specimens, and

Table 3. Smooth round bars’ mechanical properties.

#	Dia	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	in	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821449-A1	0.355	1.380	4277.907	4652.051	0.920	0.198	8,796,594.995
821449-A2	0.355	1.380	4292.754	4658.979	0.921	0.202	8,626,126.737
821449-A3	0.355	1.354	4269.989	4652.051	0.918	0.196	8,720,145.457
821449-C1	0.353	1.320	5345.533	7537.769	0.709	0.424	29,705,678.170
821449-C2	0.353	1.347	5377.829	7502.536	0.717	0.420	27,014,134.120
821449-C3	0.352	1.326	5449.583	7575.893	0.719	0.409	30,132,113.270
821449-S1	0.354	1.324	7574.631	10,504.682	0.721	0.745	16,711,196.910
821449-S2	0.353	1.322	7467.862	10,466.196	0.714	0.745	18,320,138.600
821449-S3	0.353	1.361	7518.898	10,474.047	0.718	0.751	18,439,303.770
821449-N1	0.355	1.306	7862.536	12,550.842	0.626	0.760	19,121,420.860
821449-N2	0.354	1.337	7937.811	12,554.832	0.632	0.760	18,083,595.130
821449-N3	0.355	1.343	7926.692	12,532.089	0.633	0.751	17,682,552.040

,

Table 4. Large-notched round bars’ mechanical properties.

#	Dia	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	in	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821450-A1	0.314	0.704	3980.268	4240.457	0.939	0.044	9,616,160.624
821450-A2	0.314	0.709	3953.165	4239.682	0.932	0.048	11,069,968.166
821450-A3	0.315	0.707	4000.722	4244.650	0.943	0.044	12,797,110.648
821450-C1	0.313	0.729	4898.522	6956.426	0.704	0.12	19,946,840.848
821450-C2	0.312	0.748	4845.365	6833.657	0.709	0.122	30,262,469.351
821450-C3	0.313	0.724	4881.894	6944.331	0.703	0.118	13,345,742.126
821450-S1	0.313	0.735	7969.168	9511.438	0.838	0.19	18,785,723.603
821450-S2	0.315	0.755	7894.424	9496.688	0.831	0.193	17,362,072.861
821450-S3	0.315	0.738	7480.185	9484.431	0.789	0.194	21,318,648.423
821450-N1	0.315	0.723	8200.316	11,285.144	0.727	0.193	23,047,944.727
821450-N2	0.315	0.736	8413.169	11,286.698	0.745	0.194	18,876,239.359
821450-N3	0.315	0.712	8181.671	11,270.384	0.726	0.195	26,850,255.898

,

Table 5. Small-notched round bars’ mechanical properties.

#	Dia	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	in	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821451-A1	0.314	0.68	965.641	4935.842	0.196	0.129	12,71,711.209
821451-A2	0.314	0.867	1759.371	4909.513	0.358	0.106	16,050,712.148
821451-A3	0.314	0.701	2459.403	4921.903	0.500	0.084	12,986,765.851
821451-C1	0.313	0.743	5627.409	7769.613	0.724	0.082	54,121,707.156
821451-C2	0.312	0.767	6135.583	7792.365	0.787	0.075	15,918,096.236
821451-C3	0.312	0.741	5633.366	7684.911	0.733	0.081	42,069,105.868
821451-S1	0.314	0.763	9327.301	10,643.732	0.876	0.132	29,193,423.895
821451-S2	0.314	0.740	9319.557	10,598.818	0.879	0.131	26,074,126.353
821451-S3	0.314	0.727	8932.371	10,606.562	0.842	0.131	33,524,027.986
821451-N1	0.314	0.852	1328.821	12,561.075	0.106	0.369	4,945,763.327
821451-N2	0.314	0.863	10,234.089	12,571.916	0.814	0.130	27,092,893.009
821451-N3	0.314	0.763	10,472.596	12,547.910	0.835	0.134	15,450,878.499

,

Table 6. Flat grooved plates’ mechanical properties.

#	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821452-A1	0.059	0.395	0.395	4878.669	6006.398	0.812	0.023	51,368,836.581
821452-A2	0.061	0.393	0.393	5316.193	6278.203	0.847	0.019	50,963,621.446
821452-A3	0.062	0.400	0.400	5782.864	6701.208	0.863	0.025	57,558,319.149
821452-C1	0.065	0.393	0.393	7204.201	11,264.579	0.640	0.050	124,669,693.95
821452-C2	0.059	0.396	0.396	6893.364	10,509.869	0.656	0.046	152,642,809.197
821452-C3	0.066	0.400	0.400	7239.322	11,370.277	0.637	0.047	172,211,518.364
821452-S1	0.067	0.402	0.402	8172.546	15,922.176	0.513	0.099	72,862,399.585
821452-S2	0.058	0.388	0.388	6815.095	14,240.835	0.479	0.068	69,683,745.267
821452-N3	0.066	0.396	0.396	7681.684	15,865.930	0.484	0.103	79,713,570.421
821452-N1	0.059	0.402	0.402	6977.259	15,276.174	0.457	0.108	95,627,451.873
821452-N2	0.064	0.408	0.408	7659.696	15,600.275	0.491	0.102	68,141,176.099
821452-N3	0.061	0.393	0.393	7203.887	15,478.888	0.465	0.104	87,713,646.095

,

Table 7. Cylinders’ mechanical properties.

#	D	H	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{y}}$	${\mathbf{\delta }}_{\mathbf{u}}$	E
	in	in	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$	%	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821453-A1	0.495	0.738	3180.000	3570.000	2.203	2.450	296,658.40
821453-A2	0.495	0.484	3150.000	3550.000	1.964	2.160	301,401.02
821453-A3	0.495	0.485	3150.000	3530.000	2.000	2.470	302,302.71
821453-C1	0.495	0.454	3860.000	6670.000	9.157	9.070	845,547.66
821453-C2	0.495	0.484	3700.000	6240.000	8.963	8.910	750,046.21
821453-C3	0.495	0.484	3600.000	6450.000	9.886	9.890	934,570.24
821453-S1	0.495	0.484	3230.000	11,020.000	37.199	37.200	694,362.02
821453-S2	0.495	0.486	3290.000	10,880.000	35.682	35.650	688,168.14
821453-S3	0.495	0.487	3270.000	11,070.000	36.957	36.950	436,191.96
821453-N1	0.495	0.484	4140.000	11,340.000	29.439	29.430	877,367.25
821453-N2	0.495	0.490	3830.000	11,170.000	31.748	31.740	753,100.29
821453-N3	0.495	0.492	3850.000	11,300.000	32.653	32.630	666,908.71

,

Table 8. Simple shear plates’ mechanical properties.

#	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821455-A1	0.074	0.48	2.649	1121.904	1259.496	0.891	0.065	296,658.397
821455-A2	0.075	0.484	2.672	1142.269	1287.319	0.887	0.058	301,401.023
821455-A3	0.075	0.485	2.671	1145.813	1284.037	0.892	0.066	302,302.711
821455-C1	0.075	0.454	2.665	1305.568	2255.994	0.579	0.244	845,547.658
821455-C2	0.077	0.484	2.687	1378.916	2325.523	0.593	0.241	750,046.214
821455-C3	0.074	0.484	2.658	1289.376	2310.132	0.558	0.263	934,570.236
821455-S1	0.075	0.484	2.68	1173.701	4004.392	0.293	0.997	694,362.015
821455-S2	0.074	0.486	2.667	1183.216	3912.883	0.302	0.952	688,168.138
821455-S3	0.075	0.487	2.671	1194.367	4043.317	0.295	0.987	436,191.959
821455-N1	0.083	0.484	2.705	1651.394	4523.384	0.365	0.796	877,367.247
821455-N2	0.083	0.49	2.685	1557.661	4542.839	0.343	0.852	753,100.285
821455-N3	0.081	0.492	2.685	1535.861	4507.852	0.341	0.877	666,908.705

,

Table 9. Combined shear/tension plates’ mechanical properties.

#	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821456-A1	0.079	0.409	2.331	968.431	1215.349	0.797	0.132	832,281.655
821456-A2	0.081	0.409	2.229	988.942	1252.66	0.789	0.134	890,666.596
821456-A3	0.079	0.409	1.899	965.224	1205.729	0.801	0.133	691,293.371
821456-C1	0.082	0.411	1.945	1396.804	2351.454	0.594	0.192	1,822,654.444
821456-C2	0.082	0.413	1.942	1410.333	2359.531	0.598	0.195	1,633,254.013
821456-C3	0.085	0.411	1.933	1448.22	2462.322	0.588	0.196	3,718,840.121
821456-S1	0.086	0.409	1.985	1329.577	3668.648	0.362	0.527	1,662,511.026
821456-S2	0.08	0.409	1.986	1251.847	3453.146	0.363	0.509	1,593,776.192
821456-S3	0.083	0.409	1.953	1268.718	3576.705	0.355	0.522	1,644,535.049
821456-N1	0.078	0.406	2.035	1552.984	3741.711	0.415	0.434	5,926,402.967
821456-N2	0.077	0.406	1.845	1595.521	3699.985	0.431	0.442	1,253,474.147
821456-N3	0.081	0.406	1.937	1488.509	3815.937	0.39	0.461	1,206,159.936

,

Table 10. Perforated plates’ mechanical properties.

	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821457-Al	0.082	1.556	0.412	6166.965	6333.092	0.974	0.009	12,439,464.728
821457-A2	0.082	1.540	0.419	5359.324	6255.912	0.857	0.026	6,944,724.528
821457-A3	0.082	1.562	0.406	5764.280	6352.420	0.907	0.018	4,341,796.061
821457-C1	0.079	1.500	1.043	7592.520	10,221.878	0.743	0.195	30,847,104.742
821457-C2	0.078	1.559	1.043	7252.344	9880.163	0.734	0.197	25,419,419.839
821457-C3	0.080	1.544	1.043	3482.361	8479.432	0.411	0.103	1,711,556.987
821457-S1	0.078	1.556	0.921	7018.712	13,390.532	0.524	0.354	14,162,270.843
821457-S2	0.078	1.554	0.861	6730.903	13,346.654	0.504	0.371	14,911,234.119
821457-S3	0.077	1.555	1.667	7568.450	13,498.925	0.561	0.480	19,903,132.833
821457-N1	0.076	1.188	1.337	---	465.886	---	0.564	---
821457-N2	0.078	1.203	1.546	5866.189	10,789.798	0.544	0.511	16,733,599.938
821457-N3	---	---	---	---	---	---	---	---

,

Table 11. Dog bones’ mechanical properties.

#	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821458-A1	0.119	0.492	1.057	2410.205	2719.205	0.886	0.127	8,835,307.397
821458-A2	0.117	0.491	1.209	2407.508	2698.278	0.892	0.124	9,095,178.764
821458-A3	0.119	0.490	1.260	2412.466	2715.195	0.889	0.153	8,381,175.384
821458-C1	0.120	0.493	1.260	3486.299	4707.953	0.741	0.343	34,791,986.178
821458-C2	0.124	0.492	1.260	---	5005.706	---	---	---
821458-C3	0.124	0.492	1.129	3610.458	4801.934	0.752	0.394	25,840,196.073
821458-S1	0.125	0.493	1.090	3729.009	6183.555	0.603	0.808	21,286,240.259
821458-S2	0.127	0.493	1.153	3851.168	6242.775	0.617	0.848	23,962,341.716
821458-S3	0.123	0.493	0.981	3619.571	6066.408	0.597	0.843	23,098,337.407
821458-N1	0.121	0.500	1.244	3628.255	6873.320	0.528	0.928	24,743,565.736
821458-N2	0.119	0.500	1.189	3550.852	6795.382	0.523	1.030	23,308,688.539
821458-N3	0.119	0.502	1.145	3528.724	6745.018	0.523	0.880	19,131,482.754

,

Table 12. Pipes’ mechanical properties.

#	Dia	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	in	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821459-A1	0.357	1.276	3689.924	3947.898	0.935	0.152	8,278,609.732
821459-A2	0.355	1.300	3660.665	3910.797	0.936	0.172	5,915,770.058
821459-A3	0.355	1.373	3648.754	3887.968	0.938	0.145	9,720,127.166
821459-C1	0.352	1.234	4515.368	6290.375	0.718	0.363	18,411,926.720
821459-C2	0.351	1.272	4427.822	6147.280	0.720	0.321	20,925,648.340
821459-C3	0.350	1.387	4418.984	6232.566	0.709	0.382	17,815,912.940
821459-S1	0.350	1.335	6727.092	9093.890	0.740	0.625	16,367,409.940
821459-S2	0.356	1.266	6686.978	9120.687	0.733	0.653	16,891,779.900
821459-S3	0.355	1.221	6723.792	8993.841	0.748	0.587	13,705,976.680
821459-N1	0.355	1.248	7027.524	10,563.123	0.665	0.558	13,674,415.460
821459-N2	0.355	1.208	7042.413	10,593.893	0.665	0.540	13,355,489.330
821459-N3	0.354	1.234	7003.778	10,666.096	0.657	0.613	13,087,938.730

and

Table 13. Solid square bars’ mechanical properties.

#	T	W	GL	${\mathbf{P}}_{\mathbf{y}}$	${\mathbf{P}}_{\mathbf{u}}$	${\mathbf{P}}_{\mathbf{y}}/{\mathbf{P}}_{\mathbf{u}}$	${\mathbf{\delta }}_{\mathbf{f}}$	E
	in	in	in	$\mathbf{lbf}$	$\mathbf{lbf}$	---	%	$\raisebox{1ex}{$\mathbf{lbf}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{i}{\mathbf{n}}^2$}\right.$
821460-A1	0.353	0.353	1.185	5096.240	5826.235	0.875	0.255	9,101,935.030
821460-A2	0.355	0.354	1.211	5163.502	5874.538	0.879	0.264	8,936,386.232
821460-A3	0.355	0.355	1.206	5149.967	5871.314	0.877	0.262	10,422,068.520
821460-C1	0.355	0.355	1.209	6923.174	9372.487	0.739	0.451	18,722,281.710
821460-C2	0.353	0.354	1.185	6815.070	9302.833	0.733	0.461	27,401,749.860
821460-C3	0.354	0.355	1.216	7038.902	9326.640	0.755	0.465	35,400,020.340
821460-S1	0.355	0.354	1.191	10,454.487	13,501.985	0.774	0.662	16,291,218.380
821460-S2	0.355	0.355	1.196	10,743.610	13,595.550	0.790	0.660	15,831,217.680
821460-S3	0.354	0.355	1.196	10,307.453	13,532.146	0.762	0.659	19,320,970.920
821460-N1	0.355	0.355	1.221	7819.836	14,749.937	0.530	0.862	28,773,046.640
821460-N2	0.355	0.355	1.226	7910.574	14,747.416	0.536	0.872	21,707,651.750
821460-N3	0.355	0.355	1.216	7809.754	14,725.992	0.530	0.866	23,952,446.000

present their respective material properties. It is important to note that A denotes Aluminum 6061-T6, C indicates A36 Carbon Steel, S represents 304 Stainless Steel, and N signifies Nitronic 60.

4. Discussion

Figure 5, Figure 6, Figure 7 and Figure 8 illustrate the typical fractures observed in the round bar test samples of the four metals. While all plastic behavior is important, the evaluation focused primarily on the plastic behavior near failure. It is essential to note that even when testing nearly identical sample types under uniform conditions, the resulting curves frequently vary due to factors such as the installation of the samples before loading, slight discrepancies in specimen thickness, and minor variations in chemical composition. To improve the accuracy of the experiment and reduce errors in the results, three samples are assessed per test specimen. Considering the force–displacement curves for each set of three samples, these tests demonstrated remarkable repeatability.

Fracture was observed in all tests except for the cylindrical compression specimens (refer to Figure 26, Figure 27, Figure 28 and Figure 29), which showed no signs of fracture in any metal. Each of the compression specimens experienced significant displacement, albeit in reverse order of toughness, with Aluminum 6061-T6 demonstrating the greatest displacement. This occurred due to the hardness of the platens (17-4 PH Stainless Steel, HRC 40). During testing, the platens plastically deformed, which limited the load that could be imparted to the test specimens. To account for the platen plasticity, the platens were cut into small pull-test specimens away from the area of plastic deformation, and pull tests were performed. The resulting elastic–plastic material properties, including the platens, were then used in the compression FEA models. Additionally, Digital Image Correlation (DIC) was used to capture the overall deformation of the test accurately for comparison with the FEA models. The FEA modeling takes place in Part Two of the study. Because failure did not occur, limiting plastic strains versus triaxiality are not provided with these tests. This will be acknowledged in the final results of this study for the portion of the results that are affected. While not reaching failure, the data is beneficial as it fills in some data where there were no data. The tests showed greatly increased plastic equivalent strains in compression without failure. This data is important to evaluations where underestimating plastic strains to failure represent a conservative result. Of course, achieving failure in future tests would be a desirable result.

The simple shear plate (821455) and the combined shear/tension plate (821456) test specimens were intended to produce simple shear and combined shear/tension, respectively. Refer to Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38 and Figure 39. During testing, rotations occurred that caused a tensile component to be added to the 821455-test specimen and additional tensile loading to be added to the 821456-test specimen. These rotations were most apparent in the higher strength A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals, although all the test data remained reliable. For future testing, however, an adjustment in the test specimen geometries (gauge thickness) could minimize this issue.

5. Summary and Conclusions

Part One of the study has provided a reasonable set of test data for use in Part Two. Part Two will involve replicating the test data through FEA models of the test specimens. The FEA models then will be used to establish plastic equivalent strain and triaxiality at failure data. This approach will ultimately facilitate the development of a comprehensive material property definition that links failure strain (plastic equivalent strain) to stress triaxiality for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals. These metals are commonly used in the nuclear industry due to their favorable properties, including high strength, corrosion resistance, and radiation tolerance. They are also employed in the manufacturing of shipping containers, handling tools, and other components essential for safe and efficient nuclear reactor operation. The results from this study will aid in developing a comprehensive material property definition that links failure strain (plastic equivalent strain) to stress triaxiality, ensuring integrity, preventing structural failures, and maintaining safety.

Most of the testing occurred as planned, with minor exceptions. During the testing of the cylinder (821453), platen plasticity occurred, which limited the deformation in the test specimens. This issue was particularly pronounced during the testing of the higher toughness metals (e.g., the Nitronic 60). As a result, some additional testing was performed to help facilitate Part Two of the study. Additional testing involved slicing the platens into tension test specimens to establish their elastic–plastic material properties. This makes it possible to include elastic–plastic platen models into the FEA models performed in Part Two. This was a satisfactory solution for this research. However, for subsequent experiments, it is recommended to use platens with a higher hardness value for the 821453-specimen tests. In general, for the compression tests performed, no fracture occurred. Instead, the tests were performed to produce as much plastic strain as possible, given the limitations of the tests.

During the evaluation of the simple shear plate (821455) and combined shear/tension plate (821456), rotations occurred that added tensile loading where shear loading was desired. These rotations were most apparent in the higher-strength metals (e.g., the Nitronic 60), although all the test data remained reliable. It is recommended for subsequent experiments that an adjustment in the test specimen geometries (gauge thickness) be performed to minimize this issue.