Sourcing and Generating Design Values for Analysis, Yield and Ultimate Strength  

8 August 2024

A common question fielded by a practicing materials engineer on a structural design team would be (without a doubt) the following or a variant of: “What strength values should I use in my analysis?”  This question is usually prompted by a requirement (driven by some command media, government regulation requirement, or best practice) to demonstrate that a designed structure is not loaded beyond its limits so as to not fail in service.  Instead, the load applied to these structural materials should be only up to an amount below its maximum yield or ultimate strength.  These strengths are material properties and can be described as a number termed a design value.  Design values (whether for compression, shear, bearing, or tensile) are necessary to determine factors and/or margin of safety in an analysis to assess structural performance.  Without them, a factor and/or margin of safety cannot be concluded, making it difficult to predict if the design can meet service expectations and not fail.  The sourcing of these design values is critical to the success of the structure.  Both care and caution are needed in retrieving this vital piece of data since a misstep could lead incorrect assumptions, premature failure, and catastrophic results.  In this article, let us review common sources and generation techniques a materials engineer can turn to when determining yield and ultimate strength design values.

Authoritative Sources

The first location to consult for design values is in the form of a published authoritative source.  Most engineering fields are regulated such that design values used could be referenced from established industry standard handbooks.  Examples of sources used in aerospace would be MMPDS for metals and CMH-17 for composites, with more composite values documented through NCAMP.  These sources/handbooks are the products of decades of discussions, lessons, and negotiations within communities of engineers across private, public, and academic sectors coming together to agree (or agree to disagree) on the methods used to generate mechanical testing data and the subsequent calculation to produce values for inclusion.  In fact, MMPDS and CMH-17 not only to control the process of generating these values, but also to regulate the vocabulary used to describe these numbers as allowables in their industry.  Calculations often require a specified number of observations and lots to account for material variations within a given material form (ie volume) and across multiple lots of material (ie production).  These values may take into account conditions of environmental exposure that are known to impact properties, such as high humidity wet conditions for composites or hot thermal exposure of an aluminum alloy beyond its aging temperature.  By following their calculation process, results create a value lower than typical observations to a known probability and confidence.  So, when an engineer designs up to these values, risks of overloading are low and the structure is expected to perform in service without failure. Because of the rigorous approaches and history behind them, values from these kind of authoritative sources are the lowest risk numbers to use in any structural analysis.

Published values are convenient to a design team since investment in time and cash is not required.  Simply index a value in a book and continue with analysis activities.  However, these resources are only valuable if published values exist for materials of interest.  More often than not, strength design values being sought are not published in these default sources.  Since design could drive selections to other materials (for other reasons), these other materials may not have values in these sources.  For cases where design values are not published, regulatory command media set by the design authority or the agile and diligent design team would institute an alternate means to determine them.

Following Industry Practice

In the event that a published design value cannot be retrieved, the materials engineer is encouraged to explore the methodologies described by those authoritative handbooks and follow them to collect mechanical test data and to perform calculations on thier own.  Sampling practice, standard formulae, and available calculators become the vehicles to transform mechanical testing data sets into the values being sought.  While original spreadsheets can be created to conduct these calculations, current tools available in aerospace are MIDAS and CMH-17 STATS.  Once sufficient data is collected following handbook instructions, calculations can be conducted with the resulting earning the right to be termed an allowable to meet the design team’s needs.

At first glance, the steps to follow appear easy enough.  However, in practice, large obstacles make such simple steps difficult to execute. The large amount of observations required to conclude a value as comparable and robust as those reported by MMPDS and NCAMP is simply just expensive and time consuming.  For example, a minimum of 100 tensile tests are necessary to conclude an allowable for a metallic material per MMPDS requirements.  These methods require resources in the form of cash and time, not only in the procurement of material to test but also in the time to source and conduct these tests (be it internal to one's customer or at a test lab).  However, time horizons for concluded test results can be as long as 3-6 months (if you are lucky) or longer, beyond a few years.  Where design cycles are shorter, the likelihood of concluding an allowable may not be realistic, and other means are necessary to reduce the risk of structural failure while meeting schedule demands that pace product development.  

Modifying from Industry Practice

When authoritative handbooks and their guidance fall short because of prohibitive cost and schedule constraints, poetic license and creativity led by engineering judgment begin to take charge.  Tools from industry are leveraged to help select and/or define testing standards to measure properties of interest, and alternate calculation approaches are considered, with the following being one commonly observed practice and my default recommended general approach.  Since lot and sample counts would be less then than standard as we depart handbook recommendations, at least one lot is tested with a minimum of 6 samples (for reasons to be discussed in another article) per an appropriate test standard (ie ASTM E8 for example).  Where test data cannot be collected from direct measurement, material certification data or data sets from a material supplier have been found to be helpful sources.  A minimum observed, mean value, and standard deviation are then derived, and two simple calculations are performed: 1) Calculate 80% of the mean observed value and 2) Calculate a mean observed value minus 3 times the standard deviation.  Following these calculations, these two numbers are compared to the minimum observed, and the lowest value among them is selected to report as an available and best first approximation.  By construction, this number would be lower than the mean typical observation.  

Design values produced like this (where testing is limited than standard practice) carry more risk than allowables from published handbooks.  Depending on where and how the samples were extracted, they may not accurately represent variations that could exist in a given workpiece or among product lots like those afforded by authoritative sources.  This is certainly the case if one lot was tested without sampling specific areas of interest.  Further testing across multiple lots and locations of interest may better resolve this value towards an improved number.  Additional reduction factors may be applied to accommodate for other variations (ie weld mismatch) or deviations from the original material (ie, product form tested is different instead), but must be done so with high engineering judgment anchored by experience.  Higher in risk level, this approach provides some insight by making do with less data, and is better than reporting an uninformed estimate or (more importantly) nothing. 

Material Specification Minimums

Where additional constraints are imposed and test data cannot be collected, material specification minimums for lot acceptance could be used as a design value.  These numbers would have already been published in pre-existing definitions of the material selected to be used in the design.  They could be taken from the minimum lot acceptance criteria.  In the absence of resources to support a test campaign, specification minimums are very convenient sources for design value inspiration.  However, since it cannot be said with certainty that such values were statistically derived using the methods described above, caution is exercised using these kinds of values since they might not reflect material properties accurately.  Because this technique may not be informed by data,  this approach accepts a higher risk level in comparison to earlier described methods.

Their suitability as an assumed design value leans on the material specification or drawing and how they define lot acceptance testing and the requirements set around how and where specimens are sourced for testing.  In the case of a forging where a prolongation, or excess material, is added to the workpiece, a sample taken from the edges of the workpiece may not accurately represent performance in the main volume or location of less work where final parts are to be sourced.  In the case of an adhesively bonded joint, a witness sample may be processed in parallel with an assembly, but the witness sample may have different surface preparation steps, substrates, and curvature from the joint of interest so as to not be representative of properties in the final assembly following cure.  Where material specifications are used to inform a design value,  a orrelation between lot acceptance specimens and the material in question is recommended to be understood (since one may not always be lower than the other).  This relationship should to be validated by testing, extracting samples for direct measurement on a sacrificial part where properties are really needed to be there(if not already done so).  If this sees resistance, a reduction factor could be applied for a more conservative material properties, especially for specific locations and configurations of key interest. 

Creative License

Previous prescriptions have been presented with decreasing fidelity and increasing risk acceptance from an authoritative source, with all cases relying on data and/or previous documentation concerning the material in question.  However, one final circumstance worth considering is where no published literature, no data sets, or no material specifications available to inform a calculation or recommendation for a design value.  At this point, it is up to creative approaches to build a number that is the best estimate possible given secondary sources of information available, relying on previous engineering experience and higher judgment (of oneself or others) to construct a conservative and useful value.  While no one approach can be considered a default recommendation, some points of departure could be the following:

1. Using arguments of bounding by assuming properties of other less superior materials.  Cast and some weld material material properties, for example, are lower than wrought material properties due to a as solidified microstructure and are often a reliable lower bound.

2. Looking outside to other industries for relevant guidance.  Researching guidance from civil engineering construction, pressure vessel boiler codes, and nuclear engineering for bearing strength values for a metallic material could be considered an option.

3. A percent reduction from a known similar material in composition and manufacture.  Ceramic matrix composite materials fabricated from sophisticated processes for matrix densification produce custom parts in a variety of shapes, sizes, and preforms. Estimating part-specific properties from parts built with flat panels with similar processes can provide initial insights.

4. Estimation and projection of unknown properties at variable conditions from known properties tested under known conditions.  Values from linear extrapolation, interpolation, or ratios from known values and unknown values have some merit, but should be used with some kind of correction or safety factor.

5. Ask someone with more experience.

These approaches and others not mentioned here produce numbers that carry the most risk since they are not rooted in direct measurement at all.  These numbers should only be exercised when diligent effort does not produce useful results that can meet a design schedule.  If these techniques are considered, a confirmation test regime downstream in the product life cycle during production (defined requirements for acceptance testing, for example) is recommended to confirm assumptions and safeguard structural integrity.

Final Thoughts

The generation of design values is frequently requested from materials engineers during the design phase of the engineering lifecycle.  Methodologies to source these numbers have been discussed, starting from low risk high fidelity industry standard numbers to higher risk lower fidelity values built from poetic license.  In any case, the primary objective of sourcing a conservative enough and reliable number that represents material variation is key to maximizing chances of success without failure during service.  Too liberal of a design value could lead to an overload condition, and too conservative of a design value would imply a heavier structure with higher cost.  Like any other decision made in the engineering practice, there is no right answer but many possible solutions.  Do take away that a choice informed by data sets, driving design requirements, cost and schedule, and more importantly, the cultural environment and surrounding risk tolerance, is often the best.

Thx, m