Materials Science · Selecting materials for a defined function

Service conditions and reliable property data

Useful background: Measuring and checking material claims; Elasticity, plasticity and tensile strength; Processing routes and microstructural evolution. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Select property data that represent the intended service.
Translate a load, duration, environment and permitted response into a property-data question.
Distinguish sustained-load compliance from an initial or oscillatory modulus.
Compare matched records and finite specimen distributions without relabelling a mean as a design value.
Identify which new evidence is needed when the service history changes.

A database number describes a state

A property entry should identify composition, treatment, direction, method and conditions. Temperature, duration and environment can change relevant behaviour. Use data for the intended state or justify a model connecting the available evidence to it.

Start with a specific response question. Suppose a straight polymer gauge must carry a constant axial tensile force for ten hours in a maintained warm, water-conditioned state, with an extension limit assessed at ten hours. The relevant evidence concerns deformation during that hold. A room-temperature breaking stress, an immediate stiffness and a repeated-load fatigue result answer different questions, even when their material names match.

Write the service description beside the property: material composition and lot, processing and direction, initial conditioning, temperature and surrounding medium, load history, elapsed time and response definition. Record how the gauge dimensions and extension were measured. A response value without this information cannot be transferred by its unit alone. This is the data-selection step; the geometry and load have already been specified here.

Creep is continuing deformation under sustained loading. For polymers, molecular segments can rearrange over time; temperature and absorbed fluids can change their mobility. That makes the deformation depend on the history as well as the immediate load. Viscoelasticity, temperature and time develops the underlying models. Here we select evidence for a defined history rather than fit a relaxation spectrum.

Different mechanisms require different service evidence. Hot crystalline materials can creep through defect-mediated motion, including dislocation processes, at stresses below a short-time yield value. Metals can also react electrochemically with their surroundings; iron rusting in oxygen and water is one example. A short dry test does not measure the effect of that later environment. Neither the polymer records below nor a temperature label supplies a universal degradation law.

Turn the service description into a matched record

All values and specimen records in the following comparison are invented. A and B are unnamed polymer formulations, not commercial grades. Both are tested along their prepared longitudinal direction at 60 °C after reaching a uniform equilibrium state with pure liquid water. That surrounding liquid water and temperature are maintained during the ten-hour hold. Dimensions are measured after conditioning, before loading: gauge length L₀ = 100 mm and initial area A₀ = 10.0 mm². Initial swelling is therefore already included in this reference.

A constant force P = 100 N gives nominal stress σ₀ = P/A₀ = 10.0 N/mm² = 10.0 MPa. Nominal means that the initial conditioned area is used. Treat the gauge as uniformly loaded in small axial strain; the stipulated response model neglects the small area change. Grips, joints, bending, stress concentrations, continuing chemical damage and temperature gradients are outside this gauge account. These assumptions are supplied, not established by a polymer label.

Engineering strain ε(t) is extension divided by L₀. Thus 1.00% strain means 0.0100 × 100 mm = 1.00 mm extension. The illustrative service screen is ε at ten hours ≤ 1.00%, with equality permitted. Initially compare the supplied group means; individual specimen results are examined separately below. This exact teaching screen is not a product allowable or a complete measurement decision policy.

For this constant-stress record, define apparent creep compliance J(t) = ε(t)/σ₀. It is a deformation-per-stress quotient at a named time and state. If σ is expressed in GPa, J has units GPa⁻¹; 10.0 MPa = 0.0100 GPa. Using J to predict another stress additionally requires a justified stress-response model. One record at 10 MPa alone does not establish linearity.

The table gives the mean of the same nine specimens in each formulation at three observation times. The symbol 0⁺ means immediately after the idealised rapid application of load, with any instrument contribution already removed in the supplied record. Straight joins in the figure connect these observations as reading guides; no interpolation, recovery or response after ten hours has been established.

Invented matched sustained-load group means at 10.0 MPa, 60 °C and maintained uniform water-conditioned state. Time is measured from loading; all dimensions refer to the conditioned unloaded gauge.
Time after loading	A mean strain (%)	B mean strain (%)	A J (GPa⁻¹)	B J (GPa⁻¹)
0⁺	0.200	0.300	0.200	0.300
1 h	0.600	0.450	0.600	0.450
10 h	1.500	0.800	1.500	0.800

Original invented matched group mean observations for two unnamed polymer formulations. The conditioned gauge is one hundred millimetres long and ten square millimetres in initial area. At sixty degrees Celsius and constant nominal tensile stress ten megapascals, its uniform equilibrium water-conditioned state is maintained. The horizontal axis is time after loading from zero to ten hours; zero plus denotes the immediate idealised loading response. The vertical axis is mean engineering strain in percent from zero to 1.8 percent. A uses a solid blue line and circles: 0.200 percent at zero plus, 0.600 percent at one hour, 1.500 percent at ten hours. B uses a dashed orange line and squares: 0.300, 0.450 and 0.800 percent at those times. A begins with less extension and ends with more. A horizontal long-dashed line marks the supplied one-percent mean screen, equivalent to one millimetre for this gauge. The plotted joins are reading guides between three observations, not a validated interpolation or a prediction outside the record. The same nine specimens per formulation supply the ten-hour individual records in the next figure.

Similar units can conceal different tests

A initially extends 0.200 mm and B 0.300 mm, so A is initially the less compliant formulation in this matched record. After ten hours their mean extensions are 1.50 and 0.800 mm. The ranking reverses. The ten-hour quotient for A is 0.0150/0.0100 = 1.50 GPa⁻¹; for B it is 0.800 GPa⁻¹. An initial stiffness ranking does not determine a sustained-load ranking.

A database search might return the following separate fictional records. R5 and R6 match the specified time, state, direction and response definition. The other entries remain useful for their own questions, but do not supply the missing equivalence. A specimen at the same temperature can still have a different water state, and a transverse record concerns a different material direction.

Storage modulus E′ is the ratio of the in-phase oscillating stress amplitude to the strain amplitude at a stated frequency. It is not the complete time-dependent response to applying and holding a load. Nor should a relaxation modulus measured while holding strain be silently replaced by the reciprocal of a creep compliance at the same time. The loading histories differ. A model connecting them needs more information than one isolated number.

A tempting calculation uses R1: σ/E = 0.0100/6.00 = 0.001667, or 0.1667% strain. Its arithmetic is correct for the stated elastic quotient; its transfer to the warm conditioned ten-hour question is unsupported. R2 would give 0.600% at ten hours, but describes dry A. Selecting a favourable number cannot repair the state mismatch.

Separate invented candidate database records. Each entry is a representative central value under its own specified method and state. None is a design allowable. Longitudinal and transverse refer to the prepared specimen directions.
Record	Material and state	Method / time	Value	Use for the specified hold
R1	A; longitudinal, dry, 23 °C	Initial tensile modulus E	6.00 GPa	Wrong state, temperature and time
R2	A; longitudinal, dry, 60 °C	Creep compliance at 10 h	0.600 GPa⁻¹	Wrong conditioning
R3	A; transverse, water-conditioned, 60 °C	Creep compliance at 10 h	1.20 GPa⁻¹	Wrong direction
R4	A; longitudinal, water-conditioned, 60 °C	Storage modulus at 1 Hz	2.50 GPa	Different loading history / quantity
R5	A; longitudinal, water-conditioned, 60 °C	Creep compliance at 10 h	1.50 GPa⁻¹	Matched mean-response record
R6	B; longitudinal, water-conditioned, 60 °C	Creep compliance at 10 h	0.800 GPa⁻¹	Matched mean-response record

Choose evidence appropriate to uncertainty

Distinguish measured distributions, typical values and design allowables. Inspect provenance and whether the sample represents the planned production. A precise-looking number is not necessarily more reliable than a transparent range.

A typical value is a stated representative value, often a central summary; the definition must be checked. In this dossier it means the arithmetic mean of nine distinct specimens, three from each of three labelled lots. A measured distribution retains the individual results and their grouping. It is not an extra specimen, and it is not the same thing as a fitted probability distribution for future production.

At ten hours, A’s observed strains are 1.20, 1.30, 1.40% from lot 1; 1.40, 1.50, 1.60% from lot 2; and 1.60, 1.70, 1.80% from lot 3. B’s are 0.60, 0.70, 0.80%; 0.70, 0.80, 0.90%; and 0.80, 0.90, 1.00%, with the same lot grouping. The means are 1.50 and 0.800%. A has zero of nine observed specimens at or below 1.00%; B has nine of nine. These are the same groups whose mean histories appear above.

Now tighten only the individual-specimen limit to 0.850%. B’s mean still lies below it, but its two 0.90% results and one 1.00% result fail. Six of nine observed specimens pass. A rule about every specimen cannot be replaced by a rule about the mean. Conversely, these nine observations do not establish that exactly two thirds of future B production will pass.

A justified design value has a declared engineering purpose and evidence basis: represented production and state, property definition, sampling and variability model, uncertainty treatment and decision requirements. A lower strength value and an upper creep-deformation value protect opposite sides of their respective constraints. There is no universal rule that turns a mean, an observed extreme or an arbitrary safety multiplier into such a value.

An interval for a population mean and an interval intended to cover a stated fraction of individual outcomes answer different statistical questions. Both require assumptions and a stated confidence interpretation. Neither is the engineering acceptance limit itself. Here we fit neither interval. The observed ranges, A 1.20–1.80% and B 0.60–1.00%, describe only the supplied specimens; they are not guaranteed bounds on untested material. Sampling, scale and extrapolation limits continues that inference question.

Original invented individual ten-hour strain observations for the same nine specimens per formulation used in the mean histories. Two panels have the same zero-to-two-percent strain scale and three labelled lots. Lot one uses circles, lot two triangles and lot three squares; small horizontal offsets keep the three observations in each lot visible and have no quantitative meaning. A has lot records 1.20, 1.30, 1.40 percent; 1.40, 1.50, 1.60 percent; and 1.60, 1.70, 1.80 percent. B has 0.60, 0.70, 0.80 percent; 0.70, 0.80, 0.90 percent; and 0.80, 0.90, 1.00 percent. A short-dashed violet line marks each group mean, 1.50 and 0.800 percent. A long-dashed light line marks the inclusive one-percent individual screen. None of the nine observed A specimens and all nine observed B specimens meet that screen. These points are finite fictional specimen observations, not a probability density, confidence interval, population bound or design allowable. All share the maintained sixty-degree-Celsius conditioned state and ten-megapascal nominal hold.

A changed service history needs a new bridge

Conditioning is part of the initial state, not simply a label on the final surroundings. Water entering polyamide 6 can produce concentration gradients, swelling and local changes in mechanical response; measurements and modelling of water distributions demonstrate why an overall water content does not identify every local state. This named example does not establish the numerical behaviour of fictional A and B or a rule for every polymer.

The main dossier avoids those evolving gradients by stipulating a uniform equilibrium state before loading and holding it fixed. Loading a dry gauge and only then exposing it to water is a different history. Total measured movement could include new swelling as well as load-related deformation. A matched unloaded control can help separate those contributions, but subtracting it requires a justified relation between loaded and unloaded states. A final matching average water content does not prove that their earlier local histories matched.

Changing duration is another change of question. No result at 10,000 h follows by multiplying a ten-hour strain by 1000: the first table already has changing deformation increments, and no long-time law was supplied. Changing temperature can change both rates and mechanisms. A time–temperature shift is an additional model to validate over the relevant states, not a universal conversion from a warm short test to years of service.

For the next worked load transfer only, supply a separate local mean-response model at the same ten-hour state: ε₁₀ = J₁₀σ for constant nominal stresses from 5.00 to 10.0 MPa inclusive, with J₁₀,A = 1.50 and J₁₀,B = 0.800 GPa⁻¹. This is an explicitly stipulated limited model, not inferred from one force record or asserted for every specimen. It supplies no change of temperature, moisture history, duration or failure mode.

A cyclic force, a held displacement and a held force also need different records. A constant-displacement joint may relax its force rather than follow the constant-force extension shown here. Repeated-load fatigue requires cycle and failure evidence. The same nominal stress magnitude does not make these histories equivalent. Sustained loads and creep mechanisms and Cyclic loading and fatigue initiation provide complementary preparation.

State what the comparison can actually decide

Under the supplied mean-response comparison, B has lower ten-hour extension and lies below the 1.00% mean limit, whereas A does not. Under the original individual-observation screen, all nine observed B specimens pass and none of A’s do. Keep both statements: the first concerns means; the second concerns these particular observed specimens. Neither authorises an untested component or a future population.

The next useful evidence follows the missing condition. For a changed production lot, obtain representative lot evidence; for a longer hold, obtain appropriate duration data or a validated mechanism-based extension; for changing humidity, retain conditioning and local-state evidence. Repeating a precise dry short-time modulus measurement does not fill any of those gaps.

Retain specimen identities, composition and processing records, orientation, test version, calibration and correction records, the actual time history and the definition of the reported value. If a database value is revised, preserve its earlier provenance and identify which comparison used it. Calibration, uncertainty and repeatability explains why extra decimal places or extra repeats do not remove a shared systematic effect.

The original hot-service strength question remains a useful check on scope. A short-time room-temperature strength may contribute to an initial-load question, but does not itself measure hot creep, environmental change or long-term stability. A reliable comparison names the question the data answer and the still-unmeasured requirements. It does not discard useful short-time evidence or promote it into a missing long-time test.

Worked examples

Work through the case

A database lists room-temperature strength but the component operates hot for years. Is that entry sufficient?

Identify the temperature and duration mismatch.
Assess creep, reaction and phase stability.
Obtain relevant service data or a justified model.

No. The entry supplies only part of the needed evidence.

Choose a record, then compute the response

For the specified 100 N, 10.0 mm², 100 mm conditioned gauge at 60 °C, which database records answer the ten-hour mean-extension question? Compare A and B against the 1.00 mm mean limit.

Nominal stress is 100/10.0 = 10.0 MPa = 0.0100 GPa. The length and area already refer to the unloaded conditioned state.
R5 and R6 match the material direction, conditioning, temperature, sustained-load time and compliance definition. R1–R4 lack at least one of those matches.
A: ε₁₀ = 1.50 × 0.0100 = 0.0150, hence δ₁₀ = 1.50 mm. B: ε₁₀ = 0.800 × 0.0100 = 0.00800, hence δ₁₀ = 0.800 mm.
B meets the supplied mean-extension screen; A does not. Initially A extended only 0.200 mm versus B’s 0.300 mm, so the initial ranking would have selected the wrong lower-extension formulation for this hold.

R5 and R6 give A 1.50 mm and B 0.800 mm at ten hours. The conclusion is a matched mean-response comparison, not a component allowable or population guarantee.

A passing mean can hide individual failures

Tighten only the ten-hour individual-specimen strain limit to 0.850%. Does B’s 0.800% mean show that all nine observed specimens pass? Preserve the lot identities.

Lot 1 has 0.60, 0.70 and 0.80%; all three lie at or below 0.850%.
Lot 2 has 0.70, 0.80 and 0.90%; only two pass. Lot 3 has 0.80, 0.90 and 1.00%; only one passes.
The finite count is 3 + 2 + 1 = 6 passes out of nine. The mean remains 7.20/9 = 0.800%.
Three supplied observations violate the individual limit despite the lower mean. This is a finite count with lot structure, not a fitted future failure probability.

No. Six of nine observed specimens pass the tighter individual rule, while the mean passes a different rule.

Transfer only inside the supplied model domain

Reduce the constant load to 80.0 N with the same conditioned dimensions, state and ten-hour duration. Use only the separately supplied 5–10 MPa local mean model. What mean extensions follow? Would its success justify 120 N?

The new nominal stress is 80.0/10.0 = 8.00 MPa = 0.00800 GPa, inside the stated model domain.
A gives ε₁₀ = 1.50 × 0.00800 = 0.0120, or δ₁₀ = 1.20 mm. B gives 0.800 × 0.00800 = 0.00640, or 0.640 mm.
Against the unchanged 1.00 mm mean limit, A still fails this model screen and B passes. The individual nine-specimen results at 100 N cannot silently be reused as new 80 N observations.
At 120 N, nominal stress would be 12.0 MPa, outside the supplied domain. Extrapolating the same coefficient would require additional support; the eight-megapascal calculation does not establish it.

A 1.20 mm and B 0.640 mm under the limited mean model. No 120 N result is established.

Try the reasoning

Does more decimal precision imply better accuracy?
Show the answer and reasoning
No.
Uncertainty and provenance determine interpretation. Reported digits describe presentation. The correction, calibration, specimen state and uncertainty still determine what can be inferred.
Why retain test method?
Show the answer and reasoning
Different definitions may yield different quantities.
Comparable units alone do not establish equivalence. A storage modulus and a sustained-load compliance refer to different histories. Even converting reciprocal units does not establish their equivalence.
Use R2 at 10.0 MPa to compute its own ten-hour strain. Why can that result not replace R5 in the main comparison?
Show the answer and reasoning
0.600%; it describes dry A, not the maintained water-conditioned state.
0.600 GPa⁻¹ × 0.0100 GPa = 0.00600. The smaller number is not evidence that the conditioning difference is irrelevant. A transfer needs a supported state relation.
At 10.0 MPa, the initial matched A strain is 0.200%. Compute its initial compliance and reciprocal initial quotient. Does the latter replace R1?
Show the answer and reasoning
J(0⁺) = 0.200 GPa⁻¹; its reciprocal is 5.00 GPa. It is not R1’s dry, 23 °C record.
0.00200/0.0100 = 0.200. Inverting gives 5.00, but changing notation cannot erase temperature and conditioning. This quotient also does not become the ten-hour stiffness.
At the original inclusive 1.00% individual limit, does B lot 3’s 1.00% observation pass? Does B’s observed maximum establish a maximum for all future specimens?
Show the answer and reasoning
It passes at equality; no future maximum follows.
The declared arithmetic criterion includes its boundary. The range 0.60–1.00% is a description of nine observations. A future-population bound requires a justified sampling/statistical and service-state basis.
For an otherwise matched gauge with the same stipulated strain response but L₀ = 200 mm, what are the ten-hour mean extensions at 10 MPa? Does the original 1 mm extension limit still correspond to 1% strain?
Show the answer and reasoning
A 3.00 mm and B 1.60 mm; 1 mm over 200 mm is 0.500%, not 1.00%.
Multiply the given strains 0.0150 and 0.00800 by 200 mm. A dimensional extension requirement and a strain requirement coincide only for the specified reference length; no geometry-independent pass can be inferred.
Within the supplied ten-hour local mean model, use a 50.0 N load on the original 10.0 mm² area. Calculate A and B’s mean extensions and identify the model boundary.
Show the answer and reasoning
A 0.750 mm and B 0.400 mm; 5.00 MPa is the included lower boundary.
50.0/10.0 = 5.00 MPa = 0.00500 GPa. Multiply by the supplied compliances and 100 mm. Both means meet the 1 mm screen, but no claim about untested stresses below 5 MPa, individual counts or later times follows.
A dry gauge is loaded first, then exposed to water. Its final average water content equals the main conditioned record. Must subtracting the initial extension reproduce the main ten-hour creep?
Show the answer and reasoning
No. The initial state and evolving local histories differ.
Water uptake can add swelling and change the local mechanical response while loading continues. Matching a final bulk average does not match the earlier spatial state. A matched unloaded control and a justified coupled model or directly relevant measurements are needed.
A report supplies a narrow confidence interval for mean ten-hour strain. Does that interval by itself contain the same stated fraction of individual specimens?
Show the answer and reasoning
No. Uncertainty in a mean and spread among individual outcomes are different questions.
A precise mean can coexist with a wide specimen distribution. A population-coverage statement needs its own interval construction, assumptions and confidence interpretation; neither interval is the engineering acceptance limit.
A database entry matches the main ten-hour hold. A new brief requires years of repeated force cycles at a different temperature. Which evidence is missing?
Show the answer and reasoning
Relevant duration, cyclic loading/failure, changed-temperature/state and production-representation evidence.
The original hold record remains evidence for its own state and time. It supplies neither a fatigue law nor a validated temperature/time transfer. Repeating only the matched short hold more precisely does not measure the missing conditions.

What to carry forward

Match data to service state and timescale.
Distinguish typical measurements from justified design values.
Keep initial, creep, relaxation and oscillatory quantities attached to their loading histories.
A mean, a finite specimen distribution, a population statement and a justified design value have different meanings.
Transfer only across conditions covered by actual evidence or an explicitly justified model.

References

Teaching resources and research supporting this lesson’s explanations and examples.