Understand and prepare for the tensile test

An everyday product illustrates which material properties matter in design: a cantilever chair.

• Stiffness. When you sit on a chair, it deflects slightly and springs back completely when you stand up. This deformation is elastic. Stiffness describes its magnitude: an excessively flexible chair feels unstable and bouncy even if it does not break. For many technical components, this is the decisive criterion, for example a machine-tool frame that must barely deform.
• Strength. If someone drops heavily into the chair or stands on it, the frame may remain bent: the deformation is now plastic. Under an even greater load, it breaks. Strength describes the loading that can be sustained before permanent deformation or failure occurs.
• Ductility. The frame is bent from a straight steel tube; in some designs, the seat shell is pressed from flat sheet metal. This deliberately causes substantial plastic deformation, yet the material must not crack. This ability to deform is called ductility. It matters for manufacturing, for example deep drawing car-body panels or drinks cans, and for safety: a ductile component visibly bends before breaking, providing warning of failure. A car's crumple zone uses this behaviour to absorb impact energy through plastic deformation.

A component's stiffness and strength depend on two things: its geometry and its material. A thicker tube is stiffer and stronger than a thinner tube of the same material. Conversely, a chair with exactly the same tube dimensions but made of aluminium instead of steel would deflect about three times as much under the same load.

Try it: a beam model of the cantilever chair

How stiff and how strong is a cantilever chair, and what role does the material play? The application represents one side of the chair as a beam model: the curved steel tube is replaced by its centreline and calculated as a frame of bending beams. These are the same tools you know from engineering mechanics (strength of materials): bending moment, second moment of area I and section modulus W of the tube cross-section.

Adjust the material, tube outer diameter and wall thickness, body mass, leaning force and the option to sit down heavily. The magnification factor makes the deformation visible, which would otherwise be only a few millimetres.

• Seat deflection: It shows how stiff the chair is.
• Frame colour: It shows the stress in the tube relative to what the material can withstand without permanent deformation. Green means a large reserve; red means the limit for permanent deformation has been exceeded. This illustrates strength.

The application uses quantities introduced in later sections: the stress in the tube (Section 5), Young's modulus E and the yield strength (Section 6). These are precisely the material properties supplied by a tensile test. Without them, neither the chair's deformation nor its load capacity could be calculated.

Observe and compare

Start with the prepared experiments and consider these questions:

• What changes when you replace steel with aluminium, and what stays the same?
• What happens when you sit down heavily?
• How must you change the tube to make an aluminium chair as stiff as a steel chair, and how much does it then weigh?

Return to this model after Section 6. Use the material properties to explain the differences between the settings.

Stiffness and strength are independent properties: with the same geometry, a higher-strength steel can show the same elastic deformation as structural steel while withstanding a greater load without permanent deformation.

The tensile test determines a material's mechanical properties using a specimen that is pulled slowly, without shocks (quasi-statically), until it fractures. Specimen shape, test procedure and evaluation are standardised, for metals at room temperature in DIN EN ISO 6892-1, so that results from different testing laboratories can be compared.

The specimen

The standard permits several specimen geometries, particularly round and flat specimens of different dimensions. They share two gripping sections with a larger cross-section and a gauge section with a smaller cross-section between them, connected by gently rounded transitions. The smaller cross-section ensures that the material is most heavily loaded in the gauge section: this is where it deforms and fractures, rather than at the grips, where clamping introduces additional, uneven loading.

Before testing, two quantities used in the evaluation are carefully determined:

• the initial gauge length \(L_0\), over which elongation is measured,
• the initial cross-section \(S_0\), calculated from diameter \(d_0\) for round specimens and from width \(b_0\) and thickness \(a_0\) for flat specimens.

For comparable elongation after fracture, the standard requires a fixed relationship between gauge length and cross-section. Such specimens are called proportional specimens (section 6 explains why this matters):

DIN 50125 specifies standard geometries, for example form \(A\) (round specimen with plain ends), form B (round specimen with threaded ends) and form \(E\) (flat specimen with heads).

The testing machine

One crosshead is fixed; the other moves away slowly and steadily, extending the specimen until it fractures. Two quantities are recorded continuously:

• force \(F\), using a load cell,
• elongation \(\Delta L\) in the gauge section, using an extensometer with knife edges in direct contact with the specimen, or a contactless camera system (video extensometry or digital image correlation).

The extensometer measures much more accurately than crosshead travel, because crosshead travel also includes the compliance of the grips and machine frame.

Standards at a glance: DIN EN ISO 6892-1 (tensile testing of metals at room temperature) · DIN EN ISO 6892-2 (elevated temperature) · DIN 50125 (specimen shapes) · DIN EN ISO 527 (plastics) · ASTM E8/E8M (US standard for metals).

The primary measurements in tensile testing are force \(F\) and elongation \(\Delta L\). Plotting them produces the force–elongation diagram.

The curve shows what happens to the specimen:

• Elastic deformation. Force increases linearly. When unloaded, the specimen returns completely to its original shape.
• Plastic deformation with strain hardening. Above a certain force, permanent deformation begins: dislocations glide in the crystal lattice. Force now increases more gradually because dislocations hinder one another and the material strain-hardens. The specimen becomes uniformly longer and thinner throughout the gauge length.
• Necking. At maximum force \(F_m\), strain hardening can no longer compensate for the continuous reduction in cross-section. Deformation concentrates at one location, producing a clearly visible neck. From this point, further extension requires progressively less force.
• Fracture. Microscopic voids form and coalesce in the neck until the specimen fractures, producing the typical cup-and-cone fracture surface in ductile metals.

The drop in force after \(F_m\) therefore does not mean that the material becomes weaker: deformation becomes geometrically unstable, and the cross-section at the neck decreases faster than strain hardening can compensate for.

Effect of specimen geometry

The force–extension curve depends on the specimen geometry as well as the material. A thicker specimen of the same material carries a higher force, while a longer specimen extends further under the same loading conditions. As with the chair frame in Section 2, the curve describes the whole component rather than the material alone. Try changing the dimensions below:

To obtain the material behaviour alone, the primary measurements are related to specimen geometry. It is not force alone that determines the loading of the material, but how that force is distributed across the cross-section. Engineering stress is therefore introduced as force divided by the initial cross-section:

This simple calculation is valid because the gauge section has a uniform, uniaxial stress state. Stress measures the loading of the material: under the same force, the material in a thick specimen is less heavily loaded than in a thin one.

Similarly, engineering strain is elongation divided by the initial gauge length:

It measures material deformation independently of the gauge length. The primary measurements thus become secondary quantities, producing the characteristic stress–strain curve of the material. Repeat the two tests above, this time in the \(\sigma\)-\(\varepsilon\) diagram:

Up to the maximum stress, the curves for the same material coincide. Beyond that point, the curve depends on specimen geometry: specimens with the same diameter and different gauge lengths have different curves during necking. Proportionally scaled specimens can still have the same curve beyond the maximum. Section 6 explains the connection with elongation after fracture.

Engineering stress and true stress

\(S_0\) and \(L_0\) are initial values and are not updated during the test; hence the term engineering. In reality, the specimen becomes thinner as it is pulled. True stress, based on the current cross-section, is therefore always greater than engineering stress and continues to rise after \(F_m\). Engineering stress falls during necking solely because it refers to the original cross-section. Standardised properties consistently use engineering quantities.

Regions of the \(\sigma\)-\(\varepsilon\) curve

The stages described in section 4 also appear in the \(\sigma\)-\(\varepsilon\) curve. Select a material and click on the regions:

The \(\sigma\)-\(\varepsilon\) curve provides the properties describing stiffness, strength and ductility. Select a material; clicking a marker highlights the corresponding explanation.

Which properties depend on the specimen?

\(E\), yield strength, \(R_m\) and \(A_g\) are determined while the specimen still deforms uniformly over its entire gauge length. They are therefore largely independent of specimen geometry.

Elongation after fracture is different: it includes the additional extension within the neck. The neck extends over roughly one to two specimen diameters; its contribution to elongation therefore increases with specimen thickness but is independent of gauge length. Relative to a short gauge length, this fixed contribution has a greater effect than relative to a long one: the shorter the gauge length in relation to cross-section, the greater the elongation after fracture. The Oliver relationship describes this approximately:

This is why proportional specimens are used (section 3), and why elongation after fracture is always stated together with specimen geometry: \(A\) for the short proportional specimen (\(L_0\) = 5,65·√\(S_0\), for round specimens \(L_0\) = 5·\(d_0\)), \(A_{11,3}\) for the long one (\(L_0\) = 11,3·√\(S_0\), for round specimens \(L_0\) = 10·\(d_0\)). Older standards, many datasheets and textbooks still call these values \(A_5\) and \(A_{10}\); they refer to the same quantities. Try the comparison in section 5: keep the diameter constant and use substantially different gauge lengths.

This section follows the virtual test and the PDF report. Bring your completed preparation report to the laboratory session. Complete the following tasks on site together with your supervisor.

In the materials lab, you will test a real specimen using the tensile testing machine. Then load the machine’s CSV file into the real-test interface. Evaluate the data in the same way as the virtual tests, with support from the lab supervisor.

• Import your measurements: load the testing machine's measurements into the test bench as a CSV file, either as primary data (\(F\), \(\Delta L\); enter specimen geometry and type as well) or as secondary data (\(\sigma\), \(\varepsilon\)).
• Evaluate and compare: determine the properties as in the virtual test and compare your real results with the PDF report from your virtual preparation. Where do the curves and properties differ, and why?
• Record metadata: record the specimen dimensions, batch and test temperature in full and note anything unusual in the report. Below in this section, you will learn how an ontology and a knowledge graph describe the data and how the data are transferred to the DataPortal.

Ontology and knowledge graph: what do these terms mean?

An ontology is a shared vocabulary with rules. For example, it defines what a specimen, material, testing machine or measured quantity is and how these things relate to each other.

A knowledge graph connects the information about your specific test. Think of a drawing with boxes and connecting lines:

• Specimen P01 is made of structural steel.
• Specimen P01 was tested using machine M01.
• A tensile strength was determined in this test.

The boxes represent objects or measured values, and the lines represent their relationships. This makes it possible to trace a result back to its specimen and machine. The platform generates this knowledge graph from your information; you do not need to program it by hand.

Research data in the HAW4Mat project

What happens to the test data you measured during tensile testing?

Universities produce measurements from tensile tests and other materials tests every semester. The HAW4Mat project collects these data so that they can be used after the lab course.

Once released, the data in the MaterialDigital DataPortal are available to other universities, researchers and companies.

What information should accompany the measurements?

Measurements need context. To calculate stress and strain from force and extension, you need the initial cross-sectional area \(S_0\) and initial gauge length \(L_0\). To interpret the results, you also need information about the material, specimen and test conditions. This additional information is called metadata.

Document the testing machine and measurement systems as well. Details of the load cell, extensometer and their calibration help establish the origin and quality of the measurements. The relevant calibration standards are DIN EN ISO 7500-1 for the force-measuring system and DIN EN ISO 9513 for the extensometer. A real test therefore includes two files:

• The original CSV from the testing machine contains measured values, such as force and elongation. The available columns depend on the machine export.
• versuch.ttl – what the numbers mean: specimen (\(d_0\), \(L_0\), \(S_0\)), material and batch, standard and test temperature, testing machine with force transducer and extensometer, the properties determined and the units of the CSV columns.

The descriptions are saved as RDF/Turtle, a file format for the relationships in the knowledge graph. You do not need to write this code for the practical course.

ex:specimen a h4m:Specimen ;
    h4m:shape "round, proportional" ;
    h4m:initialDiameter    [ h4m:value 10.0  ; h4m:unit unit:MilliM ] ;
    h4m:initialGaugeLength [ h4m:value 50.0  ; h4m:unit unit:MilliM ] ;
    h4m:initialCrossSection [ h4m:value 78.54 ; h4m:unit unit:MilliM2 ] ;
    h4m:madeOf ex:material .

A shared vocabulary makes it easier to compare data from different laboratories. A valid comparison also needs to account for material condition, specimen geometry and test conditions.

FAIR: four requirements for good research data

• Findable: each dataset has a unique name and keywords that can be used as filters.
• Accessible: it is clear how the data can be accessed. Once publicly released, they can be downloaded from the portal.
• Interoperable: shared formats and vocabulary allow data from different sources to be combined.
• Reusable: complete metadata and an open licence (CC BY 4.0) permit reuse.

Give the dataset a descriptive name

A dataset's name shows where it came from:

haw4mat-hso-s235jr-ws2526-zug-g03p02

Initiative · university · material · semester · test type · group and specimen. The individual components also serve as keywords for filtering the portal, for example all S235JR tensile tests from one semester.

The route into the portal

After the real test, the measurement data are exported and described using metadata. Both files are initially uploaded privately to the portal. The dataset is released publicly only after the responsible person at the university has reviewed it. Approval and transfer are carried out with the laboratory staff; you do not need to install anything.

Your role

To make your results understandable and traceable, follow these steps:

• Take measurements carefully. Record anything unusual in the report, such as fracture at the grip or an extensometer that has slipped.
• Record the metadata in full, particularly the specimen dimensions, batch and test temperature.
• Compare your material properties with the reference values in Section 7. Consider the material condition and specimen geometry, and explain any differences.
• Before publication, check whether the files or metadata contain personal information. Use group identifiers rather than students’ names in publicly released datasets.

At the real test bench, “Database” shows the saved tests and their knowledge graphs. Under “DataPortal upload”, you check the files and information with the laboratory staff before transfer.