True Stress - True Strain Curve: Part One

Sommario:

During stress testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, obtained from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample. The nature of the curve varies from material to material.

A typical stress-strain curve is shown in Figure 1. If we begin from the origin and follow the graph a number of points are indicated.

Figure 1: A typical stress-strain curve


Point A: At origin, there is no initial stress or strain in the test piece. Up to point A Hooke's Law is obeyed according to which stress is directly proportional to strain. That's why the point A is also known as proportional limit. This straight line region is known as elastic region and the material can regain its original shape after removal of load.

Point B: The portion of the curve between AB is not a straight line and strain increases faster than stress at all points on the curve beyond point A. Point B is the point after which any continuous stress results in permanent, or inelastic deformation. Thus, point B is known as the elastic limit or yield point.

Point C & D: Beyond the point B, the material goes to the plastic stage till the point C is reached. At this point the cross- sectional area of the material starts decreasing and the stress decreases to point D. At point D the workpiece changes its length with a little or without any increase in stress up to point E.

Point E: Point E indicates the location of the value of the ultimate stress. The portion DE is called the yielding of the material at constant stress. From point E onwards, the strength of the material increases and requires more stress for deformation, until point F is reached.

Point F: A material is considered to have completely failed once it reaches the ultimate stress. The point of fracture, or the actual tearing of the material, does not occur until point F. The point F is also called ultimate point or fracture point.

If the instantaneous minimal cross-sectional area can be measured during a test along with P and L and if the constant-volume deformation assumption is valid while plastic deformation is occurring, then a true stress-strain diagram can be constructed.

The construction should consist of using the equation ε = log (L/L0) for true strain in the elastic and initial plastic regions and the equation ε= log (A0/A) once significant plastic deformation has begun. In practice, however, the equation ε= log (A0/A) is used for the entire strain range since the amount of error introduced is usually negligible. The equation σ = P/A for true stress is valid throughout the entire test.

Accurate construction of a true stress-strain diagram becomes exceedingly difficult if the plastic deformation cannot be assumed to occur at a constant volume.

Finally, it should be mentioned that the neither the true stress-strain diagram nor the engineering stress-strain diagram accounts for the fact that the state of stress within the necked-down region is multiaxial. There is no simple way to account for the effect of this multiaxial state of stress on the material’s response, so it is customarily ignored. A schematic representation of an engineering stress-strain diagram and the corresponding true stress-strain diagram can be found in Figure 2.

Figure 2: Material properties determined from stress-strain diagrams: (a) Engineering stress-strain diagram; (b) determination σ by the offset method; (c) true stress-strain diagram

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Questo Articolo fa parte di una serie di Articoli di tecnologia metallurgica. È possibile fare clic sui link qui sotto per saperne di più su questo argomento.

Il Modulo opzionale Extended Range di Total Materia include una raccolta unica al mondo di curve Stress-Strain per calcoli in campo plastico relativi a migliaia di leghe metalliche, per differenti Trattamenti Termici e temperature di lavoro. Curve "true" e "engineering" sono fornite per varie velocità di deformazione ove applicabili.

Trovare un grafico Stress-Strain nel database è semplice e richiede solo pochi secondi.

Per prima cosa occorre inserire la Designazione della lega che interessa nel campo di Ricerca Rapida. Opzionalmente si può restringere la ricerca selezionando il Paese / Normativa dalla lista a discesa, e poi si clicca su "Invio".


Dopo aver selezionato il materiale di interesse, occorre cliccare sul collegamento "Curve Stress-Strain" per visualizzare i dati relativi al materiale selezionato. Il numero dei dati (diagrammi) disponibili viene visualizzato tra parentesi accanto al link.


Perché le curve Stress-Strain sono neutrali rispetto alle Normative, è possibile visualizzare i diagrammi cliccando sul link relativo per ogni Sottogruppo.

Oltre le curve Stress-Strain a diverse temperature, i dati sono forniti in forma di tabella che è esportabile a un software CAE come testo.


È anche possibile visualizzare curve Stress-Strain e relativi dati numerici per diverse temperature di lavoro.

Per fare questo, è sufficiente inserire una nuova temperatura nella casella specifica compresa nei limiti definiti e dare Invio.

Dopo aver fatto clic sul pulsante "Calcola", viene generata una nuova curva e i valori nella tabella corrispondono ora alla nuova temperatura. Si veda l'esempio qui sotto per 250°C.


Per consentirvi di testare il Database Total Materia "senza impegno", vi invitiamo a unirvi alla comunità degli Utenti registrati per i test gratuiti a Total Materia.