Embed Size (px)
Citation preview
1
THE RELEVANCE OF THE YIELD STRESS/ TENSILE STRESS RATIO IN MODERN MECHANICAL TESTING REQUIREMENTS
BY MICHAEL WRIGHT *
ROBERT GLODOWSKI**
SYNOPSIS As more varieties of high strength steels are being considered in the design of new structures, a question has arisen over the relevance of the yield-tensile ratio on the advanced behaviour of steels. The yield-tensile ratio has been a standard requirement in many Global standards for many years now, and has served its purpose well in traditionally made lower strength level steels. However, it may not be the optimum parameter required to define the behaviour of today’s steels in the inelastic zone of the tensile load-elongation curve. The shape of the engineering stress-strain (load-elongation) curve varies for different steel types. High strengths steel microstructures in the market today can have continuous yield curves, or with extended yield plateaus, or a combination of both of these curvatures. The region of the engineering stress strain curve between the elastic limit and the ultimate tensile strength can vary considerably in shape, height and length, and yet can all appear the same if evaluated simply by using the yield-tensile ratio. The behaviour of the steels inside the plastic deformation zone is becoming more important for the design of structures to withstand the impact of unexpectedly high forces that may occur in an irregular manner, such as seismic events or explosive forces. The yield-tensile ratio may be too simple to assist in understanding and defining the required properties of the steel in this region of the stress-strain curve. A more sophisticated material property measurement may be required.
Keywords:
* Bachelor Applied Science (Materials), University of Technology, Sydney, Australia Managing Director- Modern Metal Solutions Pte Ltd, Singapore. [email protected]
** Bachelor of Science in Metallurgical Engineering, South Dakota School of Mines and Technology, Principal – RJG Metallurgical, LLC., Pittsburgh, PA, USA.
2
Introduction: The mechanical properties calculated parameter Yield to Tensile Ratio (YTR) was introduced to Standards in the 1960’s (1) and is appearing more frequently in materials specifications, Standards and codes. It is readily determined from certified Standard Tensile testing results, although it is a calculated figure and not a direct measurement, and due to this it can be applied in integrity measurement situations. But what is the “Yield to Tensile Ratio” in reality?
The term “Yield Point” defines the level of Engineering Stress (load/original cross sectional area) that needs to be applied to a steel sample so that it ceases to behave in an elastic manner.
The term “Tensile” refers to the tensile strength which is defined by the maximum amount of Engineering Stress that can be applied to a steel before the load starts to drop and failure occurs.
A ratio is “the quantitative relation between two amounts showing the number of times one value contains or is contained within the other“.
This calculated parameter was implemented in the 1960’s to set a minimum level on how many multiples of the yield point it was necessary to be able to stress a metal beyond its yield without it failing for it to be considered a “ductile” material. The concept of the YTR itself is simple and easy to determine. Establishing a required value for pass or fail, and defining why this particular test value has relevance to the material performance may be less easy to understand. For example, Table 1 shows requirements for 6 different steels, all increasing in yield strength, but with the same YTR requirement. Because this is a ratio, the minimum UTS increases further as Yield increases, and so the “separation” between the Yield and the UTS is increasing. This is actually requiring the steel producer to be able to metallurgically manipulate the steel’s UTS independently of the Yield of the material, which is not an easy thing to achieve.
Table 1: Different Steel Strengths
It needs to be remembered that this parameter was just a “convenient” way to ensure a level of separation between the yield point and the ultimate tensile strength of a conventionally produced moderate strength level steel in the 1960’s (2). In this day of high strength, technically advanced steels, it may not necessarily be the “best” way. There are other characteristics that need to be considered to give an accurate representation of the behaviour of a steel under tensile stress after the yield point has been exceeded.
3
Basic Knowledge: Going back to basics, a unique stress-strain curve exists for each material, and is found by recording the amount of strain (deformation) experienced under tensile loading of a known cross sectional area of the material (stress). An example is shown below, with critical points highlighted on the graphic:
Fig 1: Stress-strain Curve Graphic for a steel (3)
O-A: is called the “Region of Proportionality” and is a straight line which indicates that in this region, stress is linearly proportional to strain (Hooke’s Law) and the body behaves like a perfectly elastic body. The gradient of the line will be equal to the Elastic Modulus of the material. Within this zone, if the applied stress is removed, the material will return to its original shape. A-B: is the region where the elastic limit occurs, starting the transition from elastic to plastic deformation behaviour. The elastic limit is difficult to determine in a routine test. Point B: is called the Yield Strength (or Yield Point if non-uniform elongation occurs). As you increase the elongation beyond B, the resulting strain will become non-linear to the stress. That is, it ceases acting in an elastic manner. The elastic limit is therefore the lowest stress at which permanent deformation can be measured. Point C: When a material is deformed beyond its elastic limit by increased stress, the strain increases in a non-linear fashion as the material begins to behave in a plastic manner. So even if the deforming load is removed, the material will not recover its original length. The material would follow the dotted line (C-D) on the graph on gradual reduction of load. The remaining strain at zero stress is known as “permanent set”. Point E: After the yield point elongation (if any) uniform elongation begins and continues until the maximum load (Tensile Strength) is achieved.
4
Point F: The maximum engineering stress endured by the material is called the ultimate tensile strength. Beyond Point F, localized strain (necking) occurs with a continuing reduction of load. The material will eventually fracture. Generally speaking, if a large deformation takes place between the Yield point (B) and Ultimate Tensile Strength (F), the material is called “ductile”. If it fails soon after the elastic limit is crossed, it is called “brittle”.
Fig 2: Stress-strain curves (4).
Curve A on Fig. 2 shows a brittle material. It has broken at the yield point, so the yield point and ultimate tensile strength will be the same value. It has only elastic behaviour - there is no plastic behaviour. Curve B on Fig. 2 shows a high strength material, with only a minimal amount of plastic behaviour. There is some small separation between the yield point and ultimate tensile strength. Curve C on Fig. 2 shows a typical steel curve, with both elastic and plastic behaviour. Curve D on Fig. 2 shows a fully plastic material, with a very limited elastic response followed by plastic behaviour as the strain increases continuously with a low application of stress. The point of conjecture here is that current Standards & Codes specify how large this separation between Yield point and Ultimate Tensile Strength needs to be for a material to be deemed “ductile”? How do you put a figure, or a percentage, onto this? And is this a true reflection of the material’s ductility??
5
The term “ductility” refers to the ability of a material to undergo large deformations without rupturing. Ductile materials can exceed their elastic limit, and permanently deform under applied stresses but they do not fail. This prevents a total structural collapse. Brittle materials will fail suddenly with very little warning, changing loading within a structure and may lead to progressive total collapse. Ductility includes the ability to survive large deformations and a capacity to absorb energy by hysteretic behaviour. In conventional structural design, the working stress is usually a proportion of the yield stress (typically 60-80% depending upon the level of loading). This is still well inside the elastic limit of the material. It is only in cases where the yield point has been exceeded and plastic behaviour is required to prevent catastrophic failure that the YTR becomes significant. In the past, the YTR has been identified as a readily measurable and convenient way to demonstrate a material’s ability to withstand increased stress beyond the point of plastic deformation. It describes a measure of the material’s capacity to strain harden. In Figure 3, all 4 of these curves have the same YTR, but they will all exhibit different behaviour between the elastic limit and the Ultimate Tensile Stress. As defined by the YTR alone, they would be identical.
Fig 3: Different Stress-strain curves.
6
Historical Practices: The first limit for Yield to Tensile Ratio (YTR) was introduced in the 1960’s for Tubular joints. This was set at 0.67 and now is generally acknowledged as being “too severe”, but still exists as a relic that is handed down through each iteration of the Standard or Code without being questioned. Other specifications have picked up on the YTR parameter and added it into their guidelines, but there is not a large body of evidence on what the optimum YTR level may be for a given product in a set environment.
Table 2: Codes and YTR Limits
Looking at these sample Standards, the YTR requirements can be anywhere between 0.67 and 0.925 depending on code and usage. Some apparent contradictions are seen here, where the European Code for Pipeline YTR is 0.88 – 0.93 but if carrying the same dangerous goods in Steel Tankers, the YTR required is 0.85. Extending this table out for the given Standards with a defined Yield and YTR, you can calculate the minimum allowed UTS, and then calculate the “Separation” between the Yield and the UTS that would make these steels comply with the given standard.
7
Table 3: Codes, YTR and Calculations
For example, in BS 5400 Pt 3 (Bridges), a steel with:
Yield 380 MPa needs UTS of 513.5 (YTR 0.74), separation = 133 MPa.
Yield 400 MPa needs UTS of 482, (YTR 0.83), separation = 82 MPa So why does a 380 MPa Yield steel for Bridges need a much greater separation between Yield and UTS than a 400 MPa Steel to be considered fit for service? Plotting the data points from Table 2, it shows no real trend or logic behind the separation between the Yield and Tensile when it is plotted against the Yield strength in Figure 4. It can be large, it can be small.
Fig 4: Yield vs Separation.
And in the case of Rebar specifications, a 500 MPa product in the Brazilian specifications is much more forgiving that the AS/NZS standards. Which level is correct, if any? And why are they so different?
Table 4: Rebar Codes YTR Comparison
8
What options are available regarding YTR? Historically, a low YTR has been considered to provide a “high” capacity for plastic deformation, and so a safe margin against fracture. But in reality, the YTR is an indication of the level of stress the steel will sustain beyond its yield point to reach UTS, and it is represented as a factor of the original yield stress. The strain component is not taken into consideration. A typical stress-strain curve contains significantly more useful information than is commonly reported in the numerical output delivered by a Test Certificate, and the entire shape of curve and critical inflexion points should be noted and understood. Figure 5 shows a “typical” stress strain curve and has denoted key points on the curve that bear closer examination. It has divided the length of the curve along the strain axis into an elastic region, a “yielding” section, a “strain hardening” component and the final “necking” to failure. The “yielding” and “strain hardening” sections cover the section of the curve we are discussing post yield but prior to UTS.
Fig 5: Typical Stress Strain Curve.
9
What options can be seen in Figure 6 to describe the behaviour of a steel beyond its Yield point but prior to achieving UTS?
Yield plateau – this depends on the manufacturing process and the strain history of the steel and is not an intrinsic material property. It is dependent on the chemical composition, heat treatment, grain size and strain ageing. But is a yield plateau a positive feature after the steel has yielded? Test laboratories like it as it makes the yield point readily apparent. But the chart is telling us that at the Yield point, the steel is elongating with no increase in applied stress. From the viewpoint of being able to maintain dimensional values, the yield plateau should be as short as possible, and preferably have some incline.
Strain hardening is primarily due to dislocations in the steel. It occurs when the strength of a metal is increased by permanent deformation. When a material is deformed beyond its plastic limit, the dislocations will begin to move until they are stopped by something else in the crystalline lattice, such as grain boundaries or alloying elements. However, one of the most effective dislocation stoppers is another dislocation. Where dislocations run on different planes and intersect, they cannot pass through each other. The dislocations pile up against each other, and can become intertwined, preventing any further permanent deformation of that particular grain. This increases the strength of the material but reduces ductility and formability. But it produces a separation between the yield point and the UTS that is critical for achieving YTR value.
Fig 6: Plastic Region of Typical Curve.
10
Evaluating the stress strain curve depicted here, there are several alternative methods which could be proposed.
1. Looking firstly at the y-axis for applied stress, to give the steel some strength beyond yield, there needs to be separation between the Yield point and the UTS. The numerical figure for this is open to debate, and could be varied depending on the service environment intended for the steel. But to allow illustration of this example, this figure could be reasonably set at 100 MPa.
2. To complete the “box”, the x-axis of strain then needs also to be defined. The length of this box would be defined by elongation of the steel after yielding until it achieves UTS (the elongation at UTS minus elongation at yield). Again, to allow an illustration of the concept, this figure could be set at 7.5%.
This would then give minimum acceptable limits for both the stress beyond the yield point and the elongation beyond the yield point. The shaded area would now represent that “acceptable” area for a 400 MPa steel to attain its UTS value and be considered “ductile” under the nominated conditions, Figure 7. If the nominated conditions were extreme, such as in a Seismic environment, these limits may be increased – maybe up 150 MPa separation between yield point and UTS, and 10% elongation between yield and UTS – and would reflect the need for the steel to be perform at a higher level in the post yield situation.
Figure 7 –Acceptable Under under given criteria
11
Returning to our theoretical steels from Figure 3, it was shown that the “brittle” steel had a very limited area under the curve in this nominated region. Of course the ductile steel would have a very a much larger area under the curve. The “continuous curve” and “Yield plateau” steel would also have a larger area than the brittle steel, but lower than a true ductile product. Calculation of the area under the curve by Integration may even allow a numerical figure to be put to this concept of “ductility beyond yield”.
Bri
ttle
Du
cti
le
Co
nti
nu
ou
s
Yie
ld P
late
au
Figure 8 – Area under the StressStrain Curve post Yield
12
Discussion: Modern structural steels are looking to reduce weight (or “dead load”) in structures while increasing strength levels to give greater economical efficiency in design. Mobile structures / vehicles are always seeking lightweight designs that may only be realised using high strength steels. The full exploitation of these steels is being hampered by the YTR, which is increasingly being seen as an outdated conservative (but convenient) measurement from the 1960’s and appropriate only for steels from that Technical era. There is a need for a separation between Yield and UTS for design integrity. But to what extent does this need to be a factor of the yield value. Why does this degree of separation need to be intrinsically linked to the yield stress? It could just be a straight numerical figure. But it would need to be supported by a minimum level of strain required to produce this separation. Improvements in production techniques and new developments in alloying design have allowed the large scale production of high strength steels by techniques such as Thermo-mechanically Controlled Processing (TMCP), Accelerated Cooling (AC) or Quench & Temper (QT) routes. (5)These processes result in various microstructures that will actually alter the shape of the stress strain curve of a steel. The combination of strength and toughness in modern steels is primarily achieved by promoting a fine grain size for a given microstructure. These steels can have yield strengths up to 1000 MPa, and so a “typical” YTR of 0.75 would mean the UTS would need to exceed 1333 MPa. Modern processing routes have a stronger effect on impeding the movement of dislocations in the steel which governs yield strength than they do on the UTS. This means that the yield strength can be moved independantly to the UTS at this stage of the process by metallurgically sophisticated processing. However it can be difficult and there are limits to how much this seperation of UTS and YS can be managed. For each steel grade, there is likely an optimum YTR, and significant deviations fom that ratio might suggest a microstructural problem. However, the does not mean that the optimum, or characteristc, value for each grade of steel should be the same, nor does it mean that a fixed value of YTR insures an acceptable or unacceptable level of perfomance in the final application. The region of the stress-strain curve beyond the yield point of a steel is coming under closer scrutiny now with the development of new design methodologies for steel structures such as the Generalised Capacity Curve, Reference Resistance Design, and the Continuous Strength Method (6) which formally permit the full plastic resistance of a structure to be attained and exceeded. These developments are based on significant advances in computational modelling that can now treat great structural and material complexities. However, to become an effective and widespread design tool, any such new methodology requires reliable knowledge of the post-yield strain hardening characteristics of the material. At this point in time, these properties are seldom known with certainty, are not defined in any structural steel materials standard and are not guaranteed by any steel manufacturer.
13
Current knowledge of steels behaviour beyond the yield point is coming under scrutiny and needs to be understood better. In the future a traditional YTR requirement may impede steel development and most likely be inadequate for these higher computational modelling programs.
Conclusion: The YTR was introduced to Standards in the 1960’s and is now ready to be superseded by more discerning measurements of a steels behaviour beyond its Yield point. In modern steelmaking, it does not meet its required task in providing reasonable confidence of a steels behaviour, and is stifling the development on new high strength steels. It has become a barrier in the International Standards to actual production of steels, and is difficult to satisfy and yet is rarely questioned by either the steel producer of the end user. It is a relic inside the Standards that needs to be set aside.
References: 1. “Structural Integrity Assessment procedures for European Industry” British Steel
plc 1986. 2. “Brief Historical Overview of Yield Strength Determination in ACI 318”, Conrad
Paulson, 2013 3. “Stress-Strain Curve for Metallic Wire”, “Studypage.in” 4. “How does one interpret stress-strain graphs that show yielding, as shown in the
details?” QUORA 5. “Significance of the Yield Stress/tensile Stress ratio to Structural Integrity”, British
Steel plc 1986. 6. “On the gradient of the yield plateau in structural carbon steels”, Sadowski,
Rotter, Stafford, Rienke & Ummenhofer, “Elsevier”, 2017
